u. 


.  G/'/es.  y.o/O.  /&3***A  o. 


THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 

LOS  ANGELES 


//- 


STEAM  TURBINES 


Published   by  the 

Me G raw-  Hill    Boot  Company 

Ne^v  York 

Successons  to  theBookDepartmervts  of  the 

McGraw  Publishing  Company  Hill  Publishing  Company 

Publishers   of  Books  for 

Electrical  World  The  Engineering  and  Mining  Journal 

Engineering  Record  Power  and  The  Engineer 

Electric  Railway  Journal  American   Machinist 

Metallurgical  and  Chemical  Engineering 


STEAM  TURBINES 

A  SHORT  TREATISE  ON  THEORY 

DESIGN,  AND  FIELD  OF 

OPERATION 


BY 

JOSEPH  WICKHAM  ROE,  M.  E. 

MEM.  AM.  SOC.  MECH.  ENGRS.,  MEM.  AM.  INST.  MINING  ENGRS. 

ASSISTANT  PROFESSOR  OF  MECHANICAL  ENGINEERING, 

SHEFFIELD  SCIENTIFIC  SCHOOL,  YALE  UNIVERSITY. 


McGRAW-HILL   BOOK   COMPANY 

239  WEST  39TH  STREET,  NEW  YORK 

6  BOUVERIE  STREET,  LONDON.  E.  C. 

1911 


COPYRIGHT,  1911 

BY   THE 

MCGRAW-HILL  BOOK  COMPANY 


Printed  and  Electrotyped 

by  The  Maple  Press 

York,  Pa. 


Engineering 
Library 

TJ 


PREFACE. 


The  purpose  of  this  book  is  twofold,  to  provide,  first,  a  text- 
book suited  to  a  short  course  on  steam  turbines  in  engineering 
schools  and,  second,  a  book  for  the  engineer  on  the  principles 
and  general  design  of  turbines  without  going  into  refined  treat- 
ment of  the  more  difficult  problems  entering  into  their  design. 

At  the  end  of  each  article  is  given  a  short  list  of  references 
where  those  wishing  to  pursue  the  subject  will  find  it  treated 
most  thoroughly.  Other  references  are  given  among  the  prob- 
lems to  sources  available  to  most  students  and  it  is  suggested 
that  these  be  made  subjects  for  short  reports,  thus  extending  the 
reading  of  the  student  beyond  the  limits  of  the  present  text. 
The  writer  wishes  to  thank  Mr.  Geo.  A.  Orrok  of  the  New 
York  Edison  Company,  the  engineers  of  the  prominent  turbine 
manufacturers,  for  data  and  illustrations  used,  and  especially 
Mr.  C.  C.  Perry  of  the  Sheffield  Scientific  School  for  his  help  in 
the  preparation  of  the  material. 

JOSEPH  W.  ROE. 

SHEFFIELD  SCIENTIFIC  SCHOOL, 

YALE  UNIVERSITY, 

April,  l.  1911. 


713873 


TABLE  OF  CONTENTS. 


CHAPTER  I. — EXPANSION  OF  STEAM.  PAGE. 

Art.    1.— The  Energy  of  a  Jet 1 

"      2. — The  Temperature-entropy  Diagram 4 

"      3. — The  Heat-entropy  Diagram 7 

"      4.— The  Velocity  of  a  Jet 9 

"      5. — Weight  of  Steam  Delivered  and  Impulsive  Force .    .  13 

CHAPTER  II. — UTILIZATION  OF  KINETIC  ENERGY  IN  STEAM. 

Art.     6. — Expanding  Nozzles 16 

"       7. — Design  of  an  Expanding  Nozzle 22 

"       8.— Blade  Forms  and  Blade  Velocities 26 

9. — Conditions  of  Maximum  Efficiency .  29 

"     10.— The  Trajectory  of  the  Steam  .    .    : 35 

CHAPTER  III. — CALCULATIONS  OF  TURBINE  BLADING. 

Art.  11. — Single-stage  Impulse  Turbines 40 

"     12. — Multi-stage  Impulse  Turbines      44 

"     13. — Single  Flow  Impulse-reaction  Turbines 54 

"     14.— Double  Flow  Impulse-reaction  Turbines 66 

CHAPTER  IV. — MECHANICAL  PROBLEMS. 

Art.  15. — Centrifugal  Strains 73 

"     16.— Bearings 78 

"     17.— Governing 82 

CHAPTER  V. — COMPARISON  OF  TYPES. 

Art.  18.— Vertical  Turbines      88 

"     19.— Tangential  Flow  Turbines 91 

"     20.— Multicellular  Turbines  ...... 94 

"     21. — Special  Forms  of  Impulse-reaction  Turbines     ...  98 

"     22. — Low  Pressure  Turbines  and  Regenerators  .    .    .    .    .  101 

CHAPTER  VI. — CONDITIONS  OF  OPERATION. 

Art.  23.— Effect  of  Superheat 108 

"     24. — High  Vacuums  in  Engines  and  Turbines 110 

CHAPTER  VII. — THE  POSITION  AND  FIELD  OF  THE  STEAM  TURBINE. 

Art.  25. — Relative  Economy  of  Engines  and  Turbines  .    .    .    .116 

"     26. — General  Comparison  of  Engines  and  Turbines.    .  126 

"     27.— Relative  Fields  of  Engines  and  Turbines 131 

INDEX 137 

vii 


STEAM  TURBINES. 


STEAM  TURBINES. 


CHAPTER  I. 

THE  FREE  EXPANSION  OF  STEAM. 
Art.  i.—  The  Energy  of  a  Jet. 

The  power  developed  in  a  steam  turbine  is  derived  from  one 
or  more  jets  of  steam.  The  power  available  depends  on  the 
kinetic  energy  of  the  steam  available  under  the  given  conditions 
of  operation. 

The  total  kinetic  energy  in  a  moving  mass  of  weight  W  and 
velocity  V  is 

WV2 

(1) 

where  the  body  is  brought  to  rest.  Where  the  velocity  is 
reduced  from  V  to  Vl  the  kinetic  energy  available  in  the  change 
is 


Or,  from  the  standpoint  of  the  force  of  the  jet  we  have  Ft  —  mV. 
Taking  the  time  as  unity  the  impulsive  force  acting  for  one 
second  is 

WV 

F=mV  =  -—-  .  (3) 

9 

If  A  =  area  of  the  jet  and  w=  the  weight  per  cubic  foot  of  the 
steam  at  the  given  pressure  and  dryness  or  superheat,  the 
weight  delivered  per  second  is  W  =  wAV.  Substituting,  Eq.  (3) 
becomes 

'  (4) 


2  STEAM  TURBINES. 

For  any  given  pressure  and  dryness  w  is  known.  Both  the 
impulsive  force  and  the  kinetic  energy,  K,  available  become 
determinate  as  soon  as  V  is  known.  An  important  part  of  the 
theory  of  turbines  has  for  its  object  the  determination  of  this 
V  for  any  given  set  of  conditions. 

Taking  the  weight  of  steam  in  Eq.  (1)  as  unity  we  have, 
since  the  value  of  2g  is  a  known  constant,  a  definite  relation 
between  K  and  7  by  which  the  velocity  V  may  be  calculated 
when  the  energy  available  per  pound  of  steam  is  known. 

The  energy  of  a  gas  such  as  steam  may  exist  in  two  forms,  heat 
and  kinetic  energy.  It  may  consist  wholly  of  heat.  In  this 
condition  the  gas  is  confined  and  under  pressure  from  the  energy 
of  its  particles,  due  to  heat.  If  allowed  to  do  so  it  would  expand 
into  a  medium  at  lower  pressure,  doing  work;  but  since  it  is 
confined  and  at  rest,  this  capacity  for  work  is  potential  only  and 
analogous  to  that  of  a  weight  suspended  and  doing  no  work,  but 
capable  of  doing  it  if  released. 

Or,  theoretically,  having  been  allowed  to  expand  under  the 
influence  of  its  heat  tension  or  pressure  until  all  the  heat  had 
been  expended,  the  energy  would  be  wholly  kinetic.  This  condi- 
tion, however,  is  unattainable,  and  is  analogous  to  the  energy  of 
the  weight  if  it  had  fallen  freely  from  its  point  of  suspension  to 
the  center  of  the  earth.  Practically,  therefore,  there  is  a  third 
or  intermediate  condition  where  the  energy  exists  in  both  forms, 
and  the  total  energy  of  the  steam  is  the  sum  of  its  heat  energy 
and  the  kinetic  energy.  As  the  weight  can  fall  only  to  the  sur- 
face of  the  ground,  so  steam  in  expanding  can  not  give  up  all  its 
heat,  but  can  part  with  it  only  to  a  point  corresponding  to  the 
temperature  of  the  medium  into  which  it  expands. 

In  the  British  system  of  units  heat  is  measured  in  British 
Thermal  Units  and  energy  in  foot-pounds,  the  two  being  inter- 
changeable at  the  ratio  of  1  B.T.U  =  777.5  foot-pounds.1  From 
the  Law  of  Conservation  of  Energy  the  total  energy  in  a  pound 
of  steam  during  expansion  remains  a  constant.  Expressing 
this  in  the  form  of  an  equation, 

WV  2  WV^ 

777.5Sl+    £  -m.5H.+HJ. 

i  The  heat  values  throughout  this  book  are  those  given  in  Marks  and  Davis'  "Steam 
Tables  and  Diagrams." 


THE  FREE  EXPANSION  OF  STEAM.  3 

where  H^  \  and  H2V2  are  the  heat  energies  and  steam  velocity 
for  any  two  stages  of  the  expansion.  Remembering  that  W  is 
unity 

y  2_  V  2 
777.5  (H1-H2)=-±--^-.  (5) 


V  2 
In  the  expansion  of  steam  from  a  vessel    ---  may  be  neglected, 

therefore  Eq.  (5)  becomes 


in  which  V  is  the  theoretical  velocity  attained,  and  Hl  and  H2  the 
total  heat  content  in  B.  T.  U.  per  pound  of  steam  before  and 
after  expansion. 

Problems. 

1.  What  is  the  impulsive  force  when  five  nozzles  are  each  discharging 
.96  Ib.  of  steam  at  a  velocity  of  3450  ft.  per  sec.? 

2.  What  velocity  must  a  pound  of  steam  have  to  deliver  87,000  ft.  Ibs. 
of  work  per  sec.? 

3.  What  energy  per  Ib.  will  steam  give  up  when  slowed  down  from 
2150  ft.  per  sec.  to  1210  ft.  per  sec.? 

4.  What  energy  per  Ib.  of  steam  will  be  available  for  a  decrease  in 
velocity  from  3090  ft.  per  sec.  to  2150? 

5.  What  weight  of  steam  must  be  delivered  per  sec.  to  give  60,000 
ft.  Ibs.  of  work  per  sec.  when  the  velocities  before  and  after  ex- 
pansion are  2500  and  1500  ft.  per  sec.? 

6.  What  is  the  theoretical  H.  P.  of  a  jet  delivering  1.3  Ibs.  of  steam 
per  sec.  at  3500  ft.  per  sec.? 

7.  What  must  be  the  initial  velocity  of  steam  which  delivers  in  one 
jet  40  H.  P.  per  Ib.  of  steam  delivered,  the  final  velocity  being 
1600ft.  per  sec.? 

8.  What  is  the  impulsive  force  in  .092  Ib.  of  steam  moving  at  1330  ft. 
per  sec.,  also  at  3680  ft.  per.  sec.? 

9.  How  many  H.  P.  are  available  in  a  heat  drop  of  42  B.  T.  U.  per  sec.? 
10.  What  heat  drop  is  required  to  generate  a  theoretical  velocity  of 

3380ft.  per  sec.? 


4  STEAM  TURBINES. 

11.  What  is  the  H.  P.  per  Ib.  of  steam  of  a  jet  where  the  heat  drop  is 
235  B.  T.  U.? 

12.  What  is  the  heat  equivalent  in  B.  T.  U.  per  Ib.  of  the  work  done 
when  steam  is  reduced  in  velocity  from  3400  ft.  per  sec.  to  1300 
ft.  per  sec.? 

13.  How  many  B.  T.  U.'s  are  the  equivalent  of  a  H.  P.  hr.? 

References. 

THOMAS:     "Steam  Turbines." 

JUDE  :     "  The  Theory  of  the  Steam  Turbine." 

Standard  works  on  thermodynamics. 

Art.  2. — The  Temperature -entropy  Diagram. 

The  determination,  then,  of  the  theoretical  steam  velocities 
which  are  to  govern  the  design,  depends  on  the  heat  drop  in  the 
stage  considered.  This  heat  drop  may  be  calculated  analyt- 
ically from  steam  tables,  or  determined  more  conveniently,  and 
with  sufficient  accuracy,  from  the  entropy  diagrams  published 
with  steam  tables  or  the  works  on  turbine  engineering. 


J 


FIG.  1. — Temperature-entropy  diagram. 

In  the  temperature-entropy  diagram  for  steam,  the  absolute 
temperature  of  the  water  or  steam  is  shown  by  the  ordinate  of  a 
point  in  a  curve,  and  the  total  heat  per  pound  by  the  projected 
area  underneath  the  curve.  The  corresponding  abscissa  repre- 
sents a  quantity  known  as  the  entropy.  As  engine  and  turbine 


THE  FREE  EXPANSION  OF  STEAM.  5 

problems  are  concerned  with  certain  changes  in  heat  which 
never  involve  the  total  contents,  that  portion  only  of  the  diagram 
above  the  melting  point  of  ice  need  be  drawn. 

The  addition  of  a  small  amount  of  heat,  dQ,  at  some  temper- 
ature T  would  be  represented  by  the  shaded  slice,  Fig.  1,  or 

TdE  =  dQ.  (7) 

If  S  be  the  mean  specific  heat  during  a  change  the  heat  added 
is  Q=S(T1-T2),  or  for  differentials,  dQ=SdT.  Substituting, 
we  have 


(7a) 


Integrating,  the  change  of  entropy  for  a  rise  in  temperature 
from  T2  to  Tv  as  from  A  to  B,  is 


T 

e.  (8) 


Equations  (7)  and  (7a)  represent  the  curve  OB,  the  projected 
area  beneath  this  line  showing  the  heat  contents  of  water. 
When  heat  is  added  as  latent  heat  and  goes  wholly  into  changing 
the  condition,  as  during  vaporization,  the  temperature  remains 

dQ 

constant  and  Eq.  (7)  becomes  -7--  =  a  constant,  i.e.,  the  entropy 

dhi 

and  the  heat  vary  directly  and  the  curve  is  a  horizontal  straight 
line  represented  by 


As  the  latent  heat  varies  for  different  temperatures  the  corre- 
sponding horizontal  lines,  such  as  BC  ,  will  vary  in  length  and  a 
curve,  CI',  drawn  through  their  ends  will  be  the  locus  of  the 
saturation  points.  After  the  water  has  been  wholly  converted 
into  steam,  further  addition  of  heat  raises  its  temperature  and 
the  equation  of  the  curve  resumes  the  form  (8),  with  S  as  the 
variable  specific  heat  of  superheated  steam. 


6  STEAM  TURBINES. 

Expansion  through  an  orifice  or  short  nozzle  is  so  rapid  as  prac- 
tically to  give  the  conditions  of  adiabatic  expansion,  in  which 
there  is  no  exchange  of  heat  between  the  steam  and  the  walls 
surrounding  it.  Such  heat  as  is  given  up  goes  into  external 
work  only,  which  is  done  at  the  expense  of  the  internal  energy  of 
the  steam.  For  instance,  let  the  steam  be  at  the  condition 
indicated  at  C,  that  is,  at  the  temperature  Tv  and  just  dry  and 
saturated.  If  allowed  to  expand  adiabatically  to  a  lower  tem- 
perature !T2  the  vertical  line  CD"  would  indicate  adiabatic  expan- 
sion, since  any  other  line  as  CD'  or  CD"  would  have  an  area 
under  it  indicating  heat  added  to  or  subtracted  from  the  steam, 
as  heat,  during  the  expansion.  The  external  work  done,  equal 
to  the  heat  energy  represented  by  the  area  A  BCD  is  accounted 
for  by  the  lowering  of  the  quality  of  the  steam,  or  the  condensa- 
tion of  a  portion.  If  the  quality  of  the  steam  was  originally 
below  the  saturation  point,  as  at  E,  then  the  quality  at  the 
lower  pressure  will  have  some  other  value,  as  shown  by  the 
position  of  F.  If  the  steam  were  originally  superheated,  as 
indicated  at  H,  adiabatic  expansion  will  reduce  the  amount  of 
superheat  as  at  /,  or  if  continued  bring  it  to  saturation  as  at  /', 
or  if  still  further  continued  condense  part  of  the  steam  as  indi- 
cated by  the  position  of  /. 


Problems. 

(Use  standard  steam  tables,  such  as  Marks  and  Davis'.) 

1.  What  is  the  increase  in  entropy  from  water  at  65°  Fahr.  to  dry, 
saturated  steam  at  320°  Fahr.? 

2.  The  entropy  of  evaporation  at  360°  Fahr.  is  1 .0514.     What  is  the 
latent  heat  of  evaporation  for  that  point? 

3.  Referring  to  Fig.  1,  under  what  conditions  will  steam  expanding 
adiabatically  from  Tj  to  T2  have  its  quality  raised,  when  will  it 
remain  about  the  same,  when  will  it  be  lowered? 

4.  What  will  be  the  final  quality  of  steam  expanded  adiabatically  from 
the  dry,  saturated  point,  C,  140  Ibs.  gauge  pressure  to  28  inches  of 
vacuum?/*,  V,A      ,177 

5-  Given  steam  at  170  Ibs.  absolute  and  superheated  100°  Fahr.,  at 
what  pressure  will  it  be  dry  and  saturated  when  expanded  adiabat- 
ically, at  what  pressure  will  its  quality,  be  90%?  (Take  the  specific 
heat  of  superheated  steam  at  0.6.) 

6.  Given  steam  at  160  Ibs.  gauge  pressure  and  98  1/2%  quality,  what  is 


THE  FREE  EXPANSION  OF  STEAM.  7 

the  quality  or  superheat  at  atmospheric  pressure  which  corresponds 
to  the  same  total  heat? 

7.  Given  1  Ib.  of  water  at  70°  Fahr.,  what  will  be  its  condition  when 
1148  B.  T.  U.'s  have  been  added  and  its  absolute  pressure  is  27  Ibs.?  tf,  : 

8.  What  is  the  B.  T.  U.  drop  per  Ib.  for  adiabatic  expansion  from" 
150  Ibs.  gauge  pressure  and  80°  Fahr.  superheat  to  a  pressure  cor- 
responding to  28  1/2  inches  of  vacuum?-  j-ll  .^ 

References. 

THOMAS:     "Steam  Turbines." 

JUDE:     "The  Theory  of  the  Steam  Turbine." 

NEILSON:     "The  Steam  Turbine." 

MOYER:     "  Steam  Turbines." 

FRENCH:     " Steam  Turbines." 

Art.  3 — The  Heat-entropy  Diagram. 

'Prof.  Mollier  has  developed  a  heat  diagram  based  upon  the 
temperature-entropy  diagram,  but  more  convenient  to  work  with. 
Copies  of  this  chart,  for  both  British  and  Continental  units,  are 
published  with  a  number  of  the  standard  works  on  steam  turbines. 
An  excellent  one  is  published  with  Marks  and  Davis'  Steam  Tables, 
a  part  of  which,  on  a  reduced  scale,  is  reproduced  here.1 

In  this  chart  the  heat  content  of  the  steam  at  any  given  condi- 
tion of  pressure  and  dryness  or  superheat,  appears  as  the  ordi- 
nate  in  a  right-angled  co-ordinate  system,  instead  of  an  area  as  in 
the  temperature-entropy  diagram,  and  the  entropy  appears  as 
the  abscissa.  Any  condition  of  the  steam  may  be  expressed  by 
the  position  of  a  point  in  this  plane.  The  points  of  equal  pressures 
being  connected,  there  results  the  series  of  curves  of  equal 
pressures  running  upward  from  left  to  right.  Similarly,  by 
connecting  points  of  constant  dryness  and  constant  super- 
heat we  have  curves  of  constant  quality  and  superheat.  A 
vertical  line  from  an  initial  condition  to  the  pressure  line 
of  the  final  condition  shows  the  heat  drop  due  to  adiabatic 
expansion  where  there  is  no  change  in  entropy,  and  the 
heat  change  may  be  read  off  directly  on  the  scale  of  the  chart. 
Horizontal  lines  indicate  changes  at  constant  heat  or  changes  of 
condition,  and  therefore  give  the  change  in  quality  for  moist 

1  The  Marks  and  Davis  Diagrams  I,  Total  Heat-entropy  Diagram  and  II,  Tota 
Heat-pressure  Diagram,  may  be  purchased  at  $0.40  net,  from  the  publishers,  Longmans, 
Green,  and  Co.,  4th  Ave.  and  30th  St.,  New  York  City. 


8  STEAM  TURBINES. 

steam,  or  in  temperature  or  superheat  for  superheated  steam. 
As  the  theoretical  velocity  developed  in  a  nozzle  is  a  function  of 
certain  constants  and  the  heat  drop  only  (Eq.  6),  an  additional 
scale  may  be  plotted  from  which  the  velocity  corresponding  to 
the  heat  change  may  be  read  off  at  once.  A  third  scale  of  the 
foot-pounds  available  per  pound  of  steam  is  also  added,  in  which 
the  values  are  777.5  times  the  B.  T.  U.  drops. 

Problems. 

1.  What  is  final  condition  of  dry  steam  expanded  adiabatically  from 
150  Ibs.  gauge  to  1  Ib.  absolute?  J'l  7 

2.  What  will  be  the  quality,  of  a  Ib.  of  steam  at  atmospheric  pressure 
which  has  the  same  total  heat  as  steam  at  50  Ibs.  absolute  and  95% 
quality?    <?/3 

3.  Let  steam  be  expanded  adiabatically  from  170  Ibs.  absolute  and 
220°  superheat,     What  is  its  pressure  when  dr^  and  saturated?  5* 
At  what  pressure  will  it  have  a  quality  of  88%?  j^ 

4.  If  dry  steam  is  expanded  adiabatically  from  100  Ibs.  gauge  pressure 
what  would  be  its  final  condition  if  the  velocity  obtained  is  3600 
ft.  per  sec.? g\ 5  Cff  %&*' 

5.  Let  steam  be  expanded  from  140  Ibs.  gauge  and  100°  superheat  and 
attain  a  velocity  of  3500  ft.  per  sec.     How  many  ft.  Ibs.  of  work 
per  Ib.  of  steam  are  being  carried  away  as  lost  heat  in  the  exhaust? 

6.  Steam  expands  from  160  Ibs.  gauge  and  120°  superheat  to  1.5  Ibs. 
absolute  and  89%  quality.     What  would  be  the  quality  if  it  had 
expanded  adiabatically  to  the  same  pressure?/    What  is  the  cause 
of  the  increase  in  quality? 

7.  A  Ib.  of  steam  at  130  Ibs.  gauge  pressure  generates  350  H.  P.,  what 
is  the  quality  at  1  Ib.  absolute?     What  is  the  change  in  entropy? 

8.  How  many  ft,  Ibs.  of  energy  are  available  per  Ib.  in  the  adiabatic 
expansion  of  dry  steam  from  150  Ibs.  gauge  to  atmospheric  pressure, 
and  also  from  atmospheric  pressure  to  1  Ib.  absolute? 

9.  Let  dry  saturated  steam  be  expanded  adiabatically  from  100  Ibs. 
absolute  to  1  Ib.  absolute.     How  many  B.  T.  U.'s  are  available 
with  an  atmospheric  exhaust? 

10.  With  dry  steam  at  140  Ibs.  gauge  pressure  and  expanding  to  1  Ib. 
absolute,  how  many  ft.  Ibs.  per  Ib.  would  be  lost  for  a  discharge  at 
the  saturation  point  over  a  discharge  under  pure  adiabatic  expan- 
sion? 

References. 
MARKS  AND  DAVIS:     "Steam  Tables  and  Diagrams." 


THE  FREE  EXPANSION  OF  STEAM.  9 

Art.  4.— The  Velocity  of  a  Jet. 

In  calculating  the  heat  drop,  in  order  to  get  the  velocity,  H1 
is  usually  found  directly  from  the  initial  conditions.  H2,  how- 
ever, is  not  known  immediately,  as  only  one  of  the  conditions, 
usually  the  pressure,  is  directly  given.  The  dryness  or  quality 
of  the  steam  at  the  lower  pressure  must  be  determined  before 


FIG.  2. — Temperature-entropy  diagram. 


H2  is  known.  Assuming  first  an  adiabatic  drop  in  pressure,  we 
will  have  the  following  equations,  referring  to  the  entropy 
diagram,  Fig.  2: 

(9) 


=  223  . 


l-q;~  T(E'  +xEv-E") 


for  moist  or  dry  saturated  steam,  x  being  the  quality,  and 


(9a) 


for  superheated  steam,  where 


q1  and  q2—  total  of  the  liquid  at  the  initial  and  final 

pressures,  Pt  and  P2, 
L1—  latent  heat  of  vaporization  for  Pl 
Tt  and  T2  =  the  absolute  temperatures  at  initial  and 

final  pressures, 
T3  =  the  absolute  temperatures   of   the   superheat,  as 

indicated  in  Fig.  2, 
$  =  the  specific  heat  of  superheated  steam. 


10  STEAM  TURBINES. 

This  last  value  has  been  the  subject  of  extensive  experiment, 
and  is  still  open  to  discussion.  A  working  value,  in  use  by 
engineers  engaged  in  handling  superheated  steam,  is  from  .6 
to  65.  Variations  in  the  specific  heat  are  taken  into  account  in 
the  heat-entropy  chart.  As  the  heat  drop  in  the  temperature- 
entropy  diagram,  Fig.  2,  is  represented  by  the  area  ABEF, 
and  as  the  side  AB  approximates  a  straight  line,  the  figure 
may  be  assumed  to  be  a  trapezoid.  The  area  then  would 

/BE+AF\ 
be  (T^-Tjl    ----- -    J. 

With  this  assumption  (9)  reduces  to 

and  (9a)  to 

.  (10a) 


El  in  the  case  of  initially  moist  steam  is  the  entropy  BE  =  xEv, 
where  x  is  the  quality  of  the  steam  and  Ev  the  entropy  of  evapora- 
tion. For  dry  saturated  steam,  Ex  becomes  Ev,  x  being  1.  E2 
is  the  entropy  AF  or  AD  according  as  initial  steam  is  moist  or 
dry.  It  may  be  scaled  directly  from  the  entropy  diagrams  or 
found  from  steam  tables  by  adding  to  E1  the  difference  between 
the  entropy  of  the  liquids  at  7\  and  T2.  The  error  introduced 
by  using  this  trapezoidal  approximation  is  only  about  1%. 

A  nozzle  will  not,  however,  deliver  steam  at  the  full  velocity 
represented  by  the  heat  drop  between  the  inlet  and  outlet 
conditions.  Whatever  the  contour  of  the  nozzle,  frictional 
resistances  are  offered  to  the  flow,  and  the  steam  must  give  up 
some  of  its  heat  energy  in  overcoming  them.  The  heat  thus 
used  raises  the  temperature  of  the  surrounding  walls  and  of  the 
particles  of  the  steam  itself.  As  the  temperature  of  the  steam 
falls  during  further  expansion,  this  heat  re-evaporates  part  of  the 
water  of  previous  condensation  and  raises  the  quality  of  the 
steam.  If  the  frictional  work  be  sufficient  to  maintain  its  heat 
constant  during  the  fall  of  temperature,  there  is  of  course  no 
heat  drop  during  the  expansion,  and  consequently  from  Eq.  (6) 


THE  FREE  EXPANSION  OF  STEAM. 


11 


no  velocity.  Such  is  the  case  where  the  work  of  friction  is  all 
spent  in  raising  the  internal  energy  of  the  steam  as  in  a  throttling 
calorimeter,  where  the  final  velocity  is  practically  zero. 

Adiabatic  and  constant  heat  expansion  are  shown  by  the  en- 
tropy diagram,  Fig.  3.  With  steam  at  condition  E  adiabatic  ex- 
pansion would  be  shown  by  the  vertical  drop  EF,  the  heat 
drop  causing  increase  of  velocity  being  represented  by  the  area 
ABEFA.  An  expansion  at  constant  heat  would  occur  along  a 
line  EF',  such  that  the  total  heat,  shown  by  the  area  beneath 
Amn  would  at  all  times  be  equal  to  that  beneath  ABE.  At  the 


B/ 


FIG.  3. — Temperature-entropy  diagram. 

final  temperature  the  total  heat  area  beneath  AFl  being  equal 
to  that  below  ABE,  no  heat  drop  would  be  shown  and  there 
would  consequently  be  no  velocity.  Actual  expansion  in 
turbine  nozzles  occurs  along  some  such  curve  as  EK,  between 
the  adiabatic  and  this  constant  heat  line.  The  heat  drop  pro- 
ducing kinetic  energy  is  represented  by  the  difference  of  total 
heat  areas  beneath  ABE  and  AK.  Under  adiabatic  conditions 
the  area  under  AF  subtracted  from  the  total  area  under  ABE, 
gives  the  area  corresponding  to  the  available  heat  energy. 
Under  the  actual  conditions  the  area  under  AK  must  be  sub- 
tracted. The  excess  area  under  FK  represents,  then,  the  heat 
which  might  have  been  applied  to  increasing  the  velocity  of  the 
steam,  but  is  lost  energy  due  to  the  frictional  resistances.  In 
dealing  with  the  relative  areas  it  should  be  borne  in  mind  that  the 
scale  of  the  ordinates  and  the  abscissas  are  widely  different. 
If  y  be  the  percentage  of  the  heat  drop  H^  —  H2  which  is  so  lost, 
(Hl  —  H2)  (l  —  y)  will  be  the  heat  energy  converted  into  kinetic 


12  STEAM  TURBINES. 

energy,  and  this  expression  may  be  substituted  in  equations 
(6),  (10),  and  (lOo)  giving 


-  y) 


(12a) 

where  E1  and  E2  are  the  entropy  changes  for  adiabatic  expansion 
as  before. 

The  percentage  of  re-evaporation,  or  increase  in  the  quality  of 
the  steam,  FK,  is  readily  obtained.  The  lost  heat,  y(Hl  —  H2), 
is  equal  to  X2L2,  where  L2  is  the  latent  heat  of  evaporation  or 
the  area  under  AG,  and  X2  is  the  percentage  of  FK  to  AG. 
Therefore 


In  .turbine  design  y  is  usually  determined  by  experiment  for 
the  type  of  nozzle  to  be  used.  An  average  of  the  results  of 
many  investigations  gives  about  10%  as  the  value  of  y,  which 
corresponds  to  a  velocity  of  about  95%  of  the  theoretical 
velocity. 

Problems. 

1.  Let  steam  at  98  1/2%  quality  and  145  Ibs.  gauge  expand  adiabatic- 
ally  to  1.5  Ibs.  absolute,  what  is  the  velocity  obtainable  by  Eq. 
(9)?     Check  this  by  the  heat-entropy  chart. 

2.  What  velocity  is  obtainable  for  an  adiabatic  expansion  from  180  Ibs. 
absolute  and  120°  superheat  to  80  Ibs.  absolute,  and  also  from  dry 
steam  3  Ibs.  absolute  to  1  lb.? 

3.  What  velocity  is  obtainable  with  an  expansion  of  from  150  Ibs. 
gauge  and  60°  superheat  to  atmospheric  pressure,  with  an  energy 
loss  of  20%?    What  is  the  condition  of  the  exhaust? 

4.  Let  dry  steam  be  expanded  from  140  Ibs.  gauge  to  2  Ibs.  absolute. 
What  will  be  the  quality  of  the  steam  when  the  energy  loss  during 
expansion  is  14%? 

5.  What  is  the  velocity  of  steam  expanded  from  155  Ibs.  gauge  and 
50°  superheat  to  1.5  Ibs.  absolute  with  15%  energy  loss? 

6.  What  is  H.  P.  per  lb.  of  steam  represented  by  the  conditions  of 
Prob.  5? 


THE  FREE  EXPANSION  OF  STEAM.  13 

7.  What  must  be  the  initial  conditions  when  steam  expanded  to  1  Ib. 
absolute  and  90%  quality  generates  370  theoretical  H.  P.  per  Ib. 
of  steam  with  an  energy  loss  of  85  B.  T.  U.? 

8.  Construct  a  condition  curve  for  the  expansion  of  steam  from  155 
Ibs.  absolute  and  80°  superheat  to  1 . 5  Ibs.  absolute,  with  a  reheat- 
ing loss  of  15%.     What  is  the  condition  of  the  steam  at  100  Ibs., 
50  Ibs.,  and  atmospheric  pressure? 

9.  What  is  the  energy  loss  when  the  velocity  loss  is  6%? 

References. 

STODOLA:     "The  Steam  Turbine." 
THOMAS:     " Steam  Turbines." 
JTJDE  :     "  Theory  of  the  Steam  Turbine." 
MOYER:     " Steam  Turbines." 
FRENCH:     " Steam  Turbines." 

Art.  5. — Weight  of  Steam  Delivered  and  Impulsive  Force. 

Both  experiment  and  theory  show  that  fur  a  given  upper  pres- 
sure P!  there  exists  a  certain  lower  pressure  p2  called  the  critical 
pressure,  for  which  the  quantity  discharged  becomes  a  maximum, 
and  that  however  far  the  final  pressure  be  lowered  the  quantity 
delivered  is  not  materially  increased .  The  final  velocity  and  weight 
discharged  will  depend  upon  the  final  pressure  only  when  that 
pressure  is  higher  than  the  "critical  pressure"  (about  .SSpJ. 
There  exists  in  an  expansion  nozzle  for  final  pressures  lower  than 
this  critical  pressure,  a  zone  near  the  inner  end  where  the  velocity 
and  weight  of  flow  are  the  same  whatever  the  lower  pressure., 
Beyond  this  point  further  expansion  to  the  final  pressure  may 
take  place,  with  a  marked  increase  of  velocity,  but  the  quantity 
delivered  will  not  be  increased.  While  the  final  velocity  attained 
depends  on  the  final  conditions,  the  quantity  discharged  depends 
solely  on  the  critical  pressure,  provided  the  final  pressure  is  less 
than  the  critical  pressure.  This  pressure  varies  somewhat  with 
different  gases,  as  shown  below. 


Gas 


Critical  Pressure 


Dry  air 

Superheated  steam. . . 
Dry  saturated  steam 


.526Pl 
.546Pl 
.577Pl 


Moist  steam j  .  582  Pj 

The  value  for  steam  is  usually  taken  at I  .58 


14  .  ,  STEAM  TURBINES. 

It  can  also  be  shown  that  whatever  the  initial  pressure,  the 
critical  velocity  of  the  steam  in  the  throat  created  by  the  drop 
in  pressure  to  .58  pv  is  about  the  same,  and  that  for  that  and 
all  lower  final  pressures  the  theoretical  velocity  in  the  throat  is 
about  1450  feet  per  second. 

To  determine,  then,  the  weight  of  flow,  only  the  critical 
velocity  and  the  area  of  the  orifice,  or,  in  the  expanding  nozzles, 
of  the  throat,  can  be  considered.  The  weight  delivered  is 


144  v 

where  A  =  the  area  of  the  orifice,  or  least  cross  section,  in  square 
inches.,  and  v=  the  volume  in  cubic  feet  per  pound  at  the  critical 
pressure  .  58  pr  Substituting  for  V  the  value  given  in  Eq.  (10)  we 
have 


(Bi+BW'j-Tj,  (14o) 

E2  and   Tz  being  taken  for  the  critical  pressure,  and  not  the 
final  pressure. 

The  available  energy  per  pound  of  steam  multiplied  by  the 
pounds  of  steam  per  H.  P.  hour  is  equal  to  33000X60.     There- 

33000X60 

fore  the  pounds  of  steam  per  H.  P.  hour—  —   or  the 

777.  o(H  j  —  H2) 

2545 

theoretical    steam   rate   per  H.  P.  hour  =  — — .  (15) 

Hi-Ht 

This  must  be  increased  by  the  percentage  of  mechanical  losses, 
such  as  windage,  friction,  etc.,  to  obtain  the  commercial  rating. 
From  Eq.  (3)  the  impulsive  force,  F,  may  be  determined  by 
substituting  the  values  of  V  and  W  found  in  Eq.  (10)  and  (14a), 
remembering  the  E2  and  T2  in  Eq.  (10)  apply  to  the  final  pressure, 
while  in  Eq.  (14a)  they  apply,  together  with  v,  to  the  critical 
pressure.  A  simple  formula,  developed  by  Mr.  George  Wilson, 
for  determining  the  reaction  of  orifices  flowing  into  atmospheric 
pressure,  while  largely  empirical,  agrees  very  closely  with 
experimental  results.  The  reaction  =  1 . 23  p1-l4.7  pounds 
per  square  inch  of  orifice.  This  applies,  of  course,  only  to  non- 
condensing  turbines. 


THE  FREE  EXPANSION  OF  STEAM.  15 

Problems. 

1.  What  is  the  theoretical  steam  rate  of  a  turbine  having  a  heat  drop 
of  235  B.  T.  U.  per  Ib.  of  steam?  ,tC^  8 

2.  What  heat  drop  must  steam  have  to  give  a  theoretical  steam  rate  of 
18  Ibs.  per  H.  P.  hour? 

3.  A  200  H.  P.  turbine  having  eight  nozzles  has  a  heat  drop  of  250 
B.  T.  U.  per  Ib.  of  steam.     What  must  be  the  throat  area  of  nozzle 
to  pass  the  required  weight  per  sec.  when  the  initial  pressure  =  150 
Ibs.  gauge. 

4.  What  is  the  reaction  of  an  orifice  .35  sq.  inch  in  area  discharging 
from  100  Ibs.  gauge  pressure  into  the  atmosphere? 

5.  What  throat  diameter  is  required  in  a  nozzle  to  give  a  reaction  of 
-     12  Ibs.  when  expanding  from  dry  steam  at  120  Ibs.  absolute  to 

atmospheric  pressure?      ,  07  3T' 

6.  What  area  of  throat  is  required  in  a  nozzle  to  discharge  .  12  Ibs.  of 
steam  per  sec.  when  the  specific  volume  is  5 . 1  cu.  ft.?   -     ' 

7.  Steam  at  150  Ibs.  absolute  is  expanded  with  an  energy  loss  of  5% 
at  the  throat,  what  area  is  required  to  discharge  .  1  Ib.  per  sec.?.  ." 

8.  What  is  the  impulsive  force  of  the  jet  in  the  throat  for  conditions 
of  Prob.  7?   '  i 

9.  What  is  the  impulsive  force  of  the  jet  if  the  expansion  of  Prob.  7 
is  continued  down  to  1 . 5  Ibs.  absolute  with  a  total  energy  loss  of 
10%?    f,      y 


References. 


THOMAS:     " Steam  Turbines." 
MOVER:     " Steam  Turbines." 
FRENCH:     "Steam  Turbines." 


CHAPTER  II. 


UTILIZATION  OF  KINETIC  ENERGY  IN  STEAM. 
Art.  6.— Expanding  Nozzles. 

When  expanding  nozzles  are  used,  the  pressure  hi  the  throat, 
a,  can  not  be  less  than  .  58  Plt  but  having  passed  this  point, 
there  is  nothing  to  preclude  further  expansion  down  to  the 
pressure  of  the  surrounding  medium.  This  further  expansion 
increases  the  velocity  of  the  steam,  but  unless  the  flow  is  con- 
centrated in  one  direction  the  energy  will  be  dissipated,  and  for 
any  useful  purposes  lost.  The  function  of  the  divergent  nozzle 
used  in  turbine  design  is  to  direct  the  jet  issuing  from  the  throat 
in  a  definite  direction  so  that  the  kinetic  energy  generated 
may  be  made  available.  There  is  no  more  energy  in  the  flow 
froni  an  expanding  nozzle  than  from  a  simple  orifice,  but  if 


FIG.  4. — Expanding  nozzle. 

properly  proportioned  the  nozzle  allows  the  steam  to  expand 
from  the  critical  pressure  to  the  final  pressure  with  a  minimum 
of  vibration,  and  renders  the  kinetic  energy  of  the  jet  available 
along  some  definite  line  of  action. 

The  proper  proportions  for  expanding  nozzles  have  been  the 
subject  of  extensive  experiments.  The  most  notable  results 
are  those  of  Rosenhain,  Stodola,  Rateau,  and  Gutermuth,  and 
the  material  brought  out  in  these  investigations  is  so  great  that 
little  more  can  be  done  here  than  to  point  out  some  of  the 
general  results. 

For  short  nozzles,  whether  rounded  at  the  entrance,  conver- 
16 


UTILIZATION  OF  KINETIC  ENERGY  IN  STEAM.     17 


gent,  or  straight,  there  is  a  sudden  drop  of  pressure  just  beyond 
the  throat  or  entrance,  to  a  pressure  below  that  of  the  discharge 
chamber.  The  steam  returns  to  the 
pressure  of  the  exhaust  medium  in  a 
series  of  oscillations  roughly  propor- 
tionate to  the  depression,  and  de- 
creasing, as  a  damped  vibration, 
until  at  perhaps  1  or  1  1/2  times  the 
length  of  the  nozzle  the  pressure  has 
settled  down  to  that  of  the  lower 
medium.  It  is  the  function  of  a  well 
designed  divergent  nozzle  to  reduce 
these  oscillations  to  a  minimum. 
These  vibrations  are  clearly  shown  in 
Fig.  5,  taken  from  Stodola's  experi- 
ments. Fig.  6  shows  the  effect  of 
the  divergent  nozzle,  where  it  is  seen 
that  there  are  practically  no  oscilla- 
tions of  pressure  within  the  nozzle 
after  the  one  created  at  the  throat 
has  died  out.  If  the  final  pressure, 
beyond  the  nozzle,  is  either  above  or 
below  that  corresponding  to  the  ex- 
pansion within  the  nozzle,  oscillations 
will  be  set  up  in  the  exhaust  space. 
These  are  shown  clearly  from  the  ex- 
periments of  Dr.  C.  E.  Lucke,  Fig.  7,1 
which  were  made  with  a  De  Laval 
nozzle,  the  best  known  for  giving 
complete  expansion.  In  this  nozzle 
the  divergent  portion  is  conical. 
Parenty  has  deduced  mathematically 
that  the  most  efficient  curve  is  that 
of  an  ellipse  with  the  focus  in  the 
throat.  Experiments  seem  also  to 
indicate  that  the  best  form  for  the  divergent  part  is  to  have  it 
slightly  concave,  and  some  turbines  have  adopted  this  form. 
But  for  manufacturing  reasons  they  are  usually  made  conical, 
as  the  increase  in  efficiency  is  only  slight. 

'  A.  S.  M.  E.,  Vol.  XXVI.,  page  134. 
2 


FIG.  5. — Expansion  curves. 


18  STEAM  TURBINES. 

The  form  recommended  by  Rosenhain  had  the  inner  corner 
but  slightly  rounded,  and  a  straight  divergent  taper  beyond,  of 
about  1  in  10  or  1  in  12.  A  greater  efficiency  appears  to  be  obtain- 
able with  a  nozzle  which  under-expands  rather  than  one  which 
over-expands,  as  the  loss  of  energy  increases  rapidly  with  over- 
expansion.  With  a  well  proportioned  nozzle  a  velocity  efficiency 


FIG.  6.— Pressure  curves  in  an  expansion  nozzle. 

of  95%  may  be  relied  on.     Fig.  8  shows  full  size  the  contour 
of  a  De  Laval  nozzle  for  a  non-condensing  turbine. 

Mr.  Strickland  Kneass,  of  Wm.  Sellers  and  Co.,  has  made  an 
extensive  investigation  into  the  discharge  of  steam  through 
nozzles  and  arrived  at  a  form  differing  quite  markedly  from  the 
De  Laval  nozzle,  but  \^hich  has  shown  an  equally  high  if  not 
higher  efficiency.  Fig.  9  shows  a  section  of  some  of  the 
nozzles  tested  and  gives  curves  of  the  variations  in  pressure  and 


UTILIZATION  OF  KINETIC  ENERGY  IN  STEAM.     19 


velocity  for  steam  at  initial  pressures  of  20,  30,  60,  90,  and  120 
pounds. 

Taking  the  1  in  10  tube,  No.  2,  as  a  basis,  various  tapers  were 


y/tfflfyty. 


Distances  from  throat 
FIG.  7. — Pressure  curves  showing  over  expansion. 

tried.  The  angle  of  divergence,  as  we  have  already  been  led  to 
expect,  had  little  or  no  effect  on  the  inlet  half  of  the  tube.  The 
tube  was  gradually  shortened  also  from  the  outlet  end  with  the 


FIG.  8. — Section  of  a  De  Laval  nozzle — non-condensing. 

same  result.  The  divergent  curve  of  No.  5  was  calculated  to 
give  uniform  acceleration  and  to  avoid  the  losses  due  to  the 
changes  of  velocity,  shown  in  the  conical  portion  of  Nos.  3  and  4, 


20 


STEAM  TURBINES. 


and  which  were  characteristic  of  all  the  straight  tapered  forms. 
This  form,  No.  5,  gave  the  best  results.  It  is  interesting  to  note 
that  while  Rosenhain  and  others  advocate  an  only  slightly 
rounded  inlet  (see  also'Fig.  8),  Mr.  Kneass  obtained  better  results 


No.  J.  Cylindrical        No.  2  Taper,  1  In  10     No.3  Taper,  1  in  6    Nb.4  Taper,  1  In  5       No.5  Special  Curve 


\s 


FIG.  9. — Kneass'  experiments  on  nozzles. 


with  well  rounded  inlets  and  a  taper  of  1  to  6.  The  best  efficiency 
obtained  was  from  a  nozzle  proportioned  for  30  pounds  initial 
pressure  and  atmospheric  exhaust.  The  results  were  as  follows: 


Gauge 
Pressure 

Actual 
Velocity 

Theoretical 
Velocity 

Difference 

Per  Cent, 
of  Loss 

120 

2690 

2820 

130 

.046 

90 

2550 

2650 

100 

.038 

60 

2290 

2400 

110 

.045 

30 

1970 

2000 

30 

.015 

15 

1400 

1500 

100 

.066 

1 

UTILIZATION  OF  KINETIC  ENERGY  IN  STEAM.     21 

The  velocity  loss,  except  at  the  lowest  pressure,  is  within  0.5% 
and  at  the  pressure  for  which  the  nozzle  was  designed,  30  pounds, 
there  was  but  1.5%  loss.  This  test  would  indicate  that  an  ex- 
panding nozzle  should  be  designed  for  a  pressure  under,  rather 
than  over,  the  average  to  be  encountered.  The  energy  loss  from 
the  above,  being  proportional  to  the  square  of  the  velocity,  varies 
from  3%  to  13%  with  an  average  of  about  10%  as  previously 
stated. 


FIG.  10. — Nozzle  on  Kerr  turbine. 

A  form  of  nozzle  similar  to  No.  5  has  been  adopted  in  the  Kerr 
turbine.  In  this  turbine  there  is  multi-  stage  expansion  and  con- 
sequently only  a  small  pressure  drop  in  any  one  set  of  nozzles. 
Fig.  10  shows  a  longitudinal  section  of  this  nozzle. 

Problems. 

1.  Report  on  tests  and  conclusions  of   Sibley  and  Kemble  in  paper 
"  Efficiency  Tests  of  Steam-turbine  "  Nozzles.    Trans.  A.  S.  M.  E., 
vol.  xxxi,  p.  617. 

2.  Report  on  the  tests  of  Borsody  and  Cairncross.     Reported  in 
Transactions  of  A.  S.  M.  E.,  vol.  xxvi,  p.  114. 

References. 

STODOLA:     " The  Steam  Turbine." 

THOMAS:     " Steam  Turbines." 

RATEAU:     "Flow  of  Steam  through  Nozzles." 

MOYER:     "  Steam  Turbines." 

JUDE  :     "  Theory  of  the  Steam  Turbine." 

BORSODY:   AND  CAIRNCROSS:     "Pressures  and  Temperatures  in  Free 

Expansion,"  Trans.  A.  S.  M.  E.,  vol.  xxvi. 
SIBLEY  AND  KEMBLE:     "Efficiency  Tests  of  Nozzles,"  A.  S.  M.  E.,  vol. 


22  STEAM  TURBINES. 

Art.  7. — Design  of  an  Expanding  Nozzle. 

The  following  example  in  the  design  of  an  expanding  nozzle, 
worked  out  first  by  the  use  of  the  steam  tables  and  entropy  dia- 
gram, will  be  used  also  to  illustrate  the  use  of  the  heat-entropy 
diagram. 

Let  the  conditions  be  as  follows: 

Initial  steam  pressure,  =  165  pounds  absolute 

Initial  dryness  of  steam,  =98  1/2  % 

Final  steam  pressure,  =  1  pound  absolute 

Loss  of  energy  during  expansion,  y        =15% 

Weight  of  steam  discharged  per  second  =  .  092  pound 

Let  it  be  required  to  find  the  diameter  of  a  conical  nozzle  and 
the  condition  of  the  steam  at  the  points  where  the  pressures  are 
96,  75,  60,  45,  30,  15,  and  1  pound  absolute  per  square  inch.  The 
first  of  these  pressures,  96  pounds,  is  .  58  of  the  initial  pressure,  and 
is  therefore  the  "  critical  pressure  "  in  the  throat.  The  first  seven 
lines  in  the  following  table  give  the  detailed  operations  in  finding 
the  adiabatic  heat  drop.  The  letters  in  the  second  column  refer 
to  Fig.  3.  Lines  8  to  12  are  the  operations  to  determine  the 
quality  of  the  steam  at  the  various  pressures.  With  this  known, 
the  volume  of  steam  to  be  delivered  per  second  may  be  calcu- 
lated. From  this  the  areas  and  corresponding  diameters  required 
may  easily  be  obtained. 

Let  it  be  given  that  the  divergent  portion  5f  the  nozzle  is  to 
be  4  inches  long.  From  the  results  tabulated  the  nozzle  may  be 
drawn  and  the  curves  of  pressures  and  velocities  plotted  as 
shown  in  Fig.  11.  Values  for  5  pounds  and  21/2  pounds 
absolute  are  interpolated  to  assist  in  drawing  the  curves.  The 
pressure  and  velocity  for  any  point  in  the  nozzle  may  be  readily 
found  from  the  curves.  For  instance  for  the  section,  aa,  project 
downward  cutting  the  two  curves.  The  pressure  curve  will  be 
cut  at  15  pounds  and  the  velocity  curve  at  2710  feet  per  second, 
as  referred  to  their  respective  scales. 

The  operations  from  1  to  12,  requiring  considerable  time  and 
care,  may  be  arrived  at  in  a  few  moments  by  the  use  of  the  heat- 
entropy  diagram.  Fig.  12  reproduces  part  of  it  for  clearness. 
From  the  point  A,  giving  the  initial  condition  of  the  steam,  165 


UTILIZATION  OF  KINETIC  ENERGY  IN  STEAM.     23 


*       S 
8       8 


CO    IN  iH 


rH  IN     O5 


<N   rt   50        _    rt   (N  05  O 

JO   5   3     g    ^   O 


K  TO 

C5   «5   N   «  rt   n 

1-1  oo  §  5    w  rt  § 


|J 


II  i 


•Sti 


5  ll- 


ii     »   «  i  J  x  -s  x  » 


03      H  C3  .        *     •**    T!    ^ ' 

jiij  *    i*;^i 

°"M1M    -a  f-s-s     5      -3 

III     a       ? 


ill  o    g 

^  >.  >  >    <^ 


24 


STEAM  TURBINES. 


pounds  pressure  and  .  985  dryness,  drop  a  perpendicular  to  B  on 
the  line  of  the  given  final  pressure,  1  pound.  The  distance  AB, 
laid  off  on  the  heat  scale  gives  319  B.  T.  U.,  the  heat  drop  for 
adiabatic  expansion,  corresponding  with  the  calculated  value  in 
line  6  of  the  table.  But  15%  of  the  heat  drop  is  lost  in  friction. 
Laying  off  Bb'  =  .  15  of  AB,  we  have  Ab'  as  the  actual  heat  drop. 
Projecting  b'  horizontally  until  it  crosses  the  1  pound  pressure 


1"  2"  3' 

FIG.  11. — Curves  for  expanding  nozzle. 

line  as  at  b",  we  have,  reading  from  the  quality  lines,  .813  as  the 
final  dryness,  which  agrees  with  the  calculated  value  line  12. 

To  ascertain  the  condition  at  any  intermediate  pressures,  with 
B  as  a  center  and  Bb'  as  a  radius,  draw  the  arc  b'c.  Draw  a 
tangent  to  the  are  b'c  through  A.  From  the  points  d,  e,  etc., 
where  AB  cuts  the  pressure  lines  in  question,  draw  arcs  tangent 
to  Ac.  Project  the  points  d' ,  e' ,  where  the  arcs  cut  AB,  hori- 
zontally over  to  the  points  d",  e",  on  their  respective  pressure 


UTILIZATION  OF  KINETIC  ENERGY  IN  STEAM.     25 

lines.  These  points  referred  to  the  quality  lines  give  the 
dryness.  A  "quality  curve/'  Ab",  may  be  drawn  through 
d",  e",  etc.,  from  which  the  dryness  for  any  intermediate  pressure 
may  be  read  off  at  once.  The  qualities  thus  found  will  agree 
with  the  values  as  calculated  within  limits  of  error  justified  by 
the  nature  of  the  problem.  It  may  be  noted  here  that  this  qual- 
ity curve  may  be  laid  off  almost  as  readily  for  a  varying  friction 


Fio.   12. — Condition  curve  for  expanding  nozzle. 

loss  as  for  a  constant  one.  This  is  of  value  in  calculations  for 
multistage  machines  where  the  friction  losses  increase  as  the 
steam  expands. 

Problems. 

I.  Design  an  expanding  nozzle  for  the  following  conditions:  Initial 
steam  pressure  =  120  Ibs.  gauge;  superheat  =40°  Fahr. ;  atmospheric 
discharge  pressure ;  energy  loss,  16% ;  weight  of  steam  delivered  = 
.11  Ib.  per  sec. ;  length  of  nozzle  =3  ins. 


26 


STEAM  TURBINES. 


2.  Design  a  nozzle  for  same  conditions  as  Prob.  1,  except  that  dis- 
charge pressure  is  1 .5  Ibs.  absolute  and  length  =4  ins. 

3.  Calculate  the  H.  P.  available  in  jet  at  throat  of  nozzle,  Prob.  1,  and 
also  after  expansion  to  atmospheric  discharge  pressure. 

4.  Calculate  the  H.  P.  available  at  throat  and  exit  of  nozzle  in  Prob.  2. 

5.  If  the  expanding  portion  of  the  nozzle  in  Prob.  2  is  4  inches  long, 
what  are  the  pressure  and  velocity  at  points  1/2  inch  and  2  1/2 
inches  from  the  throat? 


References. 


STODOLA:     "The  Steam  Turbine." 
THOMAS:     "Steam  Turbines." 
MOYER:     "Steam  Turbines." 

Art.  8.— BLADE  FORMS  AND  BLADE  VELOCITIES. 

The  velocities  which  enter  into  the  problem  of  turbine  design 
are: 

The  absolute  velocity  of  the  jet  as  it  enters  the  blades. 

The  velocity  of  the  moving  blades. 

The  relative  velocity  of  the  jet  and  the  blades. 

The  absolute  velocity  of  the 
jet  as  it  leaves  the  blades. 

The  ideal  condition  in  all 
turbines,  whether  steam  or 
water  driven,  is  that  the  driv- 
ing fluid  "  enter  without  shock 
and  leave  without  velocity." 
Let  V,  above,  be  the  abso- 
lute velocity  of  the  entering 
steam,  and  u  the  blade  veloc- 
ity. W,  the  relative  velocity, 
is  found,  both  in  magnitude 
and  direction,  from  the  ve- 

FIG.  13. — Velocity  diagram.  ,       .  .          ,       T7  . 

locity  triangle  V,  u,  and  W. 

The  angle  /?  determines  the  direction  of  the  back  of  the  blade 
on  the  entering  side.  The  curved  surface  of  the  blade  de- 
flects the  jet,  discharging  it  backward  with  a  velocity  W1} 
equal  to  W,  less  a  certain  loss  due  to  friction.  This  friction  can 
not  be  determined  theoretically,  but  may  be  assumed  from  results 
of  experiments  and  experience  in  turbine  design.  These  indicate 
that  Wl  varies  from  .  8  to  .  95  of  W,  according  to  conditions,  .  92 
being  a  fair  average  value  for  the  single  stage  turbine.  The  angle 


UTILIZATION  OF  KINETIC  ENERGY  IN  STEAM.     27 

/?'  is  ordinarily  made  equal  to  /?  for  convenience  in  manufacture 
and  to  reduce  end  thrust.  Having  W±  in  magnitude  and  direc- 
tion, the  final  absolute  velocity  7t  is  readily  obtained  by  com- 
bining it  with  the  bucket  velocity  u.  From  equation  (2)  the  energy 

yz  _y  2 
per  pound  of  steam  developed  in  buckets  is  —         —  and  the  theo- 

2# 
retical  efficiency  is 


Fig.  14  shows  a  convenient  method  of  determining  the  form 
of  the  bucket,  where  entrance  and  exit  angles  are  equal. 

Lay  off  u,  the  bucket  velocity,  horizontally.  Draw  V  to  the 
same  scale,  making  the  angle  a.  In  the  De  Laval  wheel  this 
angle  is  20°.  Closing  the  triangle  we  have  the  relative  velocity 


e, 
f — Pitch-^ 


FIG.  14. — Determination  of  blade  sectioas. 

W  in  direction  and  magnitude.  Draw  ab  parallel  to  u  and  lay 
off  /?'  =  /?  on  the  exit  side.  Take  c  and  e  equidistant  from  ab  and 
the  width  of  the  blade  apart.  Lay  off  cc'  and  ee'  equal  to  the 
pitch  of  the  blades.  The  face  of  the  bucket  may  be  drawn  as  the 
arc  of  a  circle  about  the  intersection,  /,  of  the  perpendiculars  cf 
and  ef  and  the  center  line  ab.1  The  back  of  the  blade  is  formed 
by  two  lines  parallel  to  be  and  be  connected  by  an  arc  with /as  the 
center. 

The  best  width  ce  and  pitch  cc'  are  empirical  and  determined 
by  experience,  as  no  formulae  for  them  have  been  developed. 
Moyer  says,  "for  turbines  of  less  than  100  H.  P., the  width  of  the 

1 A  well  known  German  rule  is  to  make  the  radius  equal  to  twice  the  pitch  times  sine  /?,  or 
r  =2p  sine  )9. 


28  STEAM  TURBINES. 

blades  is  often  made  about  I",  increasing  to  about  1.5"  in  tur- 
bines of  1000  H.  P."  "The  most  efficient  blade  pitch  appears  to 
be  between  the  limits  of  1/2"  and  1".  Between  these  two  values 
the  efficiency  of  blades  made  according  to  conventional  designs 
is  practically  constant.  The  usual  blade  pitches  are  5/8,  3/4,  and 
7/8  inch." 

It  is  more  important  that  the  backs  of  thq  vanes  should  be 
parallel  to  the  entering  steam  than  the  faces,  for  steam  striking 
the  backs  is  deflected  outward,  retarding  the  wheel  and  causing 
loss.  If  it  strikes  the  face  the  energy  of  deflection  goes  into  useful 
work  in  the  wheel.  In  the  spacing  of  the  blades  there  must  be 
enough  free  area  to  provide  for  the  unobstructed  passage  of  the 
steam  at  the  large  volume  corresponding  to  the  exhaust  side  of 
the  blade,  and  it  should  be  as  near  uniform  in  section  as  con- 
ditions will  permit.  It  must  be  borne  in  mind,  too,  that  the 
opening  of  a  round  inclined  nozzle  is  an  ellipse,  and  the  greater 
part  of  the  steam  is  discharged  through  these  openings  near  the 
middle  of  the  nozzle. 

Problems. 

1.  If  steam  issues  from  a  nozzle  with  a  velocity  of  3400  ft.  per  sec.  at 
an  angle  a.  =20°  and  the  blade  velocity  u  =1200  ft.  per  sec.,  what 
are  the  relative  velocity  W  and  blade  angle  /?? 

2.  Assume  blade  angles  /?  and  /?t  as  equal,  what  is  the  final  absolute 
exit  velocity  neglecting  steam  friction  in  the  blading? 

3.  What  is  the  energy  per  Ib.  of  steam  available  for  the  conditions  of 
Probs.  1  and  2?    What  is  the  efficiency? 

4.  Given  7=3400  ft.  per  sec.  a  =20°,  w=1200  ft.  per  sec.,  and  an 
energy  loss  of  20%  in  passage  through  the  blading,  what  is  the 
final  velocity  of  exit  Fx? 

5.  Determine  the  energy  absorbed  by  the  wheel  per  Ib.  of  steam  and 
the  efficiency  for  conditions  of  Prob.  4. 

6.  Draw  a  cross  section  of  the  blading  for  conditions  of  Prob.  4. 
What  length  of  blade  could  be  used  with  a  nozzle  .8  inch  exit 
diameter? 

7.  How  many  r.  p.  m.  should  a  42-inch  diam.  wheel  run  for  a  nozzle 
velocity  of  2300  ft.  and  a  =22  1/2°  and  /?  =27°. 

8.  With  a  blade  velocity  u  =400  ft.  per  sec.,  a  nozzle  velocity  of  1720 
ft.  per  sec.,  and  a  =42°,  what  will  be  the  absolute  angle  of  exit  of  the 
steam  for  a  symmetrical  blade? 

9.  Report  on  article  on   "Principles  of  Steam   Turbine   Buckets." 
Power,  March  17,  1908,  p.  391 


UTILIZATION  OF  KINETIC  ENERGY  IN  STEAM.     29 


References. 

STODOLA:     "The  Steam  Turbine." 
THOMAS:     "  Steam  Turbines." 
MOYER:     "  Steam  Turbines." 
JUDE:     "Theory  of  the  Steam  Turbine." 
NEILSON:     "  The  Steam  Turbine." 

Art.  9.—  Conditions  of  Maximum  Efficiency. 

Let  Fig.  15  be  the  velocity  diagram  for  the  entrance  and 
exit  velocities,  where  the  relative  velocity  W  is  supposed  to 
remain  constant. 


FIG.  15. — Velocity  diagram. 

From  trigonometry 


FIG.  16. — Velocity  diagram. 


V12  =  W2  +  u2-2uW  cos 
V2-  VS  =  +  2u  W  (cos  p 
V12  =  V2-2u  W  (cos  p  + 


cos 


subtracting, 
(17) 


Y2—V  2 


The  efficiency  of  the  bucket,  -  —  —  ,  Eq.  (16),  will  be  highest 

when  Vi2  is  least.  Vl2  will  be  least,  V2  being  constant,  for  the 
maximum  value  of  the  second  term  in  Eq.  (17).  *  As  in 
hydraulic  problems  the  ideal  condition  is  given  by  complete 
reversal  where  cos  /?  and  cos  /?t  are  each  positive  and  unity. 

FIRST  CASE.  —  Where  p,  &  and  V  are  fixed. 

Since  the  above  quantities  are  fixed  it  is  clear  from  Eq.  (17) 
that  YI  is  least  where  uW  is  greatest.  In  Fig.  16  the  area  of 

abxtrn, 
the   triangle   abc  =  bc.%ac    sin    p  =  lab.cm,     therefore    —  —  —  = 


30 


STEAM  TURBINES. 


oc.oc  =  W.u.  But  ab  =  F,  and  sin  /?  are  constant,  therefore, 
comparing  with  Eq.  (17),  Ft2  is  least  when  cm  is  maximum. 
The  length  ab  and  the  angle  acb  are  fixed,  therefore  the  locus  of 
the  possible  positions  of  the  intersection  c  with  reference  to  ab  is 
an  arc  acb  and  cm  is  maximum  when  ac  =  cb,  or  when  u  —  W.  We 
have  then 

F 
U=      ^3  (18) 


and 


(19) 


Taking  the  relative  velocities  TF  and  W \  as  equal,  the  efficiency, 

F2-  F^  2w.  TF(cos  £+ cos  ft) 

— ^—  becomes  -         — ^L_ 

If,  in  addition,  /?  and  ft  are  also  equal 


FIG.  17.—  Velocity  diagram. 

Since  W  cos  p=  V  cos  a-u,  the  efficiency  in  terms  of  a  is 


(20) 


SECOND  CASE.—  Where  V  and  a  are  fixed,  and  ft  and  ft  are  equal 
but  not  determined. 

Eq.  (17)  above  becomes  Vl2  =  V2-4uWcos^,  V,2^  V2-4u.cd. 


UTILIZATION  OF  KINETIC  ENERGY  IN  STEAM.     31 

Vl  is  least  when  u.cd  is  maximum,  bd,  the  sum  of  u  and  cd  is 
constant  and  =  V  cos  a.     Therefore,  u.cd  is  maximum  for  u  =  cd,  or 


V  cos 


(21) 


and 


tan 


ad     ad       ad 

1  =  —  =  —  =  2  —  =  2  tan  a. 
dc     bd       bd 


Also,  since  W  =  Wl}  ec  =  ac  and  the  triangle  cef  can  easily  be 
shown  to  be  similar  and  equal  to  the  triangle  acd.  Therefore 
cf=  ad  or  Vl=V  sin  a. 

V2-V2                              V2-V2sin2a 
The  efficiency 2 —  becomes  then  = — 

V2  (I -sin2  a) 

2 —   —  or  simply  =cos2a  (22) 


FIG.  18. — Velocity  diagram. 

THIRD  CASE. — When  V,  a,  and  ft  are  fixed.  The  triangle  abc 
is  fixed.  W  and  u  are  therefore  determinate.  Cos  /?u  then,  is 
the  only  variable  on  the  right  hand  side  of  Eq.  (17),  and  Vl  is 
least  for  ft  =  0. 

In  the  foregoing,  losses  in  the  relative  velocity  W,  due  to  fric- 
tion, have  been  neglected.  If  these  be  considered,  V2  =  W2  + 
u2  +  2uW  cos  p  as  before,  but  Vf  becomes  V12=W1 
2uWl  cos  ft,  where  Wt=yW. 


32  STEAM  TURBINES. 

The  energy  developed  is 

72  _  V2     w*-WS  +  2u(W  c 


The  general  expression  for  the  efficiency 
V2-V12_W2-W12  +  2u  (W  cos 


l  cos  ft) 


y*  F2 

For  Case  II  where  /3  =  ft  it  becomes 

TF2  -  W*  +  2w.  cos  p  (W  +  JFj) 


(23) 


It  frequently  happens  that  the  best  value  of  u  must  be  sacri- 
ficed for  safety  or  for  cheapness  of  construction,  or  there  may 
be  offsetting  gains  in  mechanical  efficiency  by  adopting  a 


FIG.   19. — Velocity  diagram. 

slower  speed.  Take  as  an  example,  a  De  Laval  nozzle,  coming 
under  Case  II,  delivering  steam  at  3680  feet  per  second  at  an 

angle,  a  =  20°.  Then  u  =  y-  =  -— .  94  -  1730  feet  per  sec- 
ond. This  would  give  a  value  for  the  relative  velocity 

w  =  X/36802  + 17302  -  2  co8~26°~3680  . 1730  =  2130  feet, 

and  a  blade  angle,  p  =  tani  2  tan  20°=- tan'1. 728  =  36°.  Experi- 
ence has  shown  that  the  blade  velocity  should  not  exceed  1400 
feet  per  second.  If  the  actual  speed  be  1250  feet  per  second 
the  value  for  the  relative  velocity  is 


UTILIZATION  OF  KINETIC  ENERGY  IN  STEAM.     33 


W  =  A/36802  +  12502-  2  cos  20°  .3680  .1250  =  2540 
and  since  sin  /3  =     ~  -_  -  -  ,  the  blade  angle  = 
3680  sin  20° 


FIG.  20. — Velocity  diagram. 

In  the  De  Laval  turbine  a  nozzle  angle  of  20°  has  been  estab- 
lished for  all  sizes.  The  angles  /?  and  /3X  are  equal,  varying  from 
30°  or  32°  up  to  36°. 

/?  and  /?t  can  not  be  equal  to  zero,  unless  the  plane  of  the  rever- 
sal of  the  steam  makes  an  angle  with  the  line  of  motion.  This 
is  done  in  some  turbines,  as  the  Stumpf  and  Terry  machines. 


FIG.  21. — Velocity  diagram — tangential  type. 

The  introduction  of  this  new  angle  partially  offsets  the  advan- 
tage of  complete  reversal,  as  will  be  seen  in  considering  Fig.  21. 
If  V  and  u  be  represented  by  ab  and  ac  the  velocity,  u,  can  be 
resolved  into  two  components,  u  cos  a  =  ad,  and  u  sin  a  =  cd. 
The  component  cd  will  be  impressed  on  the  entering  jet  giving  it 
the  direction  ab'  so  that  W  is  the  relative  velocity  of  entrance,  not 


34  STEAM  TURBINES. 

cb  or  ef.  The  complete  reversal  of  the  jet  gives  a  relative  exit 
velocity  of  W,  equal  to  —  W,  and  an  absolute  exit  velocity 
of  V1}  as  shown. 

Neilson  shows  that  V1  is  minimum  for  u  =  — — -- .     For  this 

F2(l  -cos'a.) 
value  7,2  =  — 

3  cos2a+l 

The  third  of  the  principal  forms  of  buckets  used  in  single- 
expansion  turbines  is  the  Pelton  type,  which  lends  itself  to  use 


FIG.  22.— Pelton  type  of  blade. 

with  steam  as  well  as  water.     A  complete  reversal  of  the  steam 

y 
jet  and  a  value  of  u  =  -  would  give  a  theoretical  efficiency  of  100%. 

It  is  necessary,  of  course,  to  give  the  steam  some  exit  velocity 
to  clear  the  wheel.  This  velocity,  V1}  can  be  determined  graph- 
ically as  in  Fig.  22,  or  analytically  by  the  equation 

V*  =  W2  +  u*-'2  W  ucos  ft.     Since  W=V-u 

=  (V-u)2  +  u2-2u  (V-u)  cos  ft, 
=  V2-2u  (V-u)  (1+cos  ft). 

The  theoretical  efficiency  as  before  = 


_2u  W  (1+cos  /9) 


(25) 


UTILIZATION  OF  KINETIC  ENERGY  IN  STEAM.     35 

Problems. 

1.  Given  V  =2420  ft.  per  sec.,  /?.  =45°  and  0,  =40°,  what  is  the  best 
value  for  the  blade  velocity  and  for  the  nozzle  angle?     Neglect 
steam  friction. 

2.  What  is  the  blade  efficiency  for  the  conditions  of  Prob.  1. 

3.  Given  a  steam  velocity  of  2250  ft.  per  sec.  and  a  nozzle  angle  of 
22°,  what  is  the  best  blade  velocity,  neglecting  steam  friction? 
What  is  the  efficiency  of  the  blading? 

4.  With  symmetrical  blading  what  nozzle  angle  should  be  used  when 
the  steam  velocity  is  2700  ft.  per  sec.  and  the  blade  velocity  1430 
ft.  to  get  an  efficiency  of  87%? 

5.  What  angles  a  and  /?  should  be  used  for  a  DeLaval  nozzle  and  blade 
to  give  88  1/2%  efficiency  with  an  entrance  velocity  of  3550  ft.  per 
sec.?     What  blade  velocity  does  this  call  for? 

6.  What  is  the  power  developed  per  Ib.  of  steam  for  the  conditions  of 
Prob.  5? 

7.  Find  the  power  developed  in  a  DeLaval  blade  with  V  =3550  as  in 
Prob.  5.,  u  limited  to  1240  ft.  per  sec.,  a  =20°. 

8.  Find  the  power  developed  under  the  conditions  of  Prob.  7  if  in 
addition  there  is  a  velocity  loss  of  10%  in  passage  through  the 
blades;  what  is  the  blade  efficiency  under  these  conditions? 

9.  Show  that  for  maximum  efficiency,  V  and  u  are  at  right  angles. 
10.  Prove  that  "dilution  of  the  jet"  or  lowering  the  velocity  of  the 

steam  by  having  mixed  with  a  heavier  fluid,  as  water,  is  a  less 
efficient  way  of  reducing  speeds  than  by  lowering  the  velocity.1 

References. 

STODOLA:     "The  Steam  Turbine." 

NEILSON:     "The  Steam  Turbine." 

THOMAS:     "Steam  Turbines." 

JUDE:     "Theory  of  the  Steam  Turbine." 

MOYER:     "Steam  Turbines." 

RATEAU:  "Method  of  Calculating  Steam  Turbines,"  London  Engi- 
neering, Dec.  10,  1909,  p.  804. 

BRILING:  "Energy  Losses  in  Turbine  Buckets,"  Zeitschrift  d.  v. 
Deut.  Ing.,  Feb.  12,  1910. 

Art.  10— The  Trajectory  Of  The  Steam. 

The  absolute  direction  of  the  steam  at  any  point  may  be  deter- 
mined by  combining  the  velocity  u  of  the  vane  with  that  of  the 
steam  as  it  moves  relatively  to  the  vane.  Neglecting  frictional 
losses,  this  would  have  a  magnitude  W,  and  a  direction  tangent 

"See  French,   Steam  Turbines,  p.  63. 


36 


STEAM  TURBINES. 


to  the  vane  surface  at  the  point  in  question.  By  taking  a  suc- 
cession of  points  the  absolute  directions  chould  be  found  and  the 
envelope  of  these  would  give  an  approximate  trajectory.  The 
error  in  this  method  is  cumulative,  however,  and  a  better  way  is 
as  follows:  Let  W  be  the  relative  velocity  at  entrance,  and  u  the 
vane  velocity  as  heretofore.  If  the  inner  vane  surface  be  semi- 
circular the  time  required  to  move  from 

A  to  B  will  be  — .   The  distance  forward 


covered  in  the  time  will  be  u 


W 


Lay- 


ing  this  off  along  the  path  of  B  we  have 
the  end  of  the  trajectory.  For  any  in- 
termediate point,  as  C,  the  time  required 

arc  AC 
will  be  and  the  distance  forward 

arc  AC 
covered    by  C  will    be    CCt  =  — ==-  u. 

The  path  will  depend  on  the  size  and 
shape  of  the  vane  and  the  relative 
velocities  u  and  W.  If,  as  is  usual, 
the  vane  surface  is  only  a  portion  of  a 
semicircle,  the  method  is  not  altered  and 
the  distance  CCl  for  any  point  C  is  laid 

distance  AC 
off  along  its  path  equal  to —  — 

u,  and  so  on  for  any  number  of  points  needed  to  determine 
the  curve. 

If,  however,  the  relative  velocity  W  be  reduced  by  friction  to  Wl 
during  the  passage  through  the  vane  it  will  lengthen  out  the 
trajectory.  Just  at  what  rate  the  retardation  occurs  would  be 
difficult  to  determine,  but  it  may  be  assumed  to  be  uniform.  If 
W  and  Wl  be  the  relative  velocities  at  entrance  and  exit  the  loss 
from  A  to  B=W—W1,  and  assuming  this  loss  as  uniform  the 

AC 
velocity  at  C  =  W-  t    (W '—  WJ  and  the  time  required  to  move 


Fio.  23. — Trajectory  of  the 
steam. 


from  A  to  C 


AB 

AC 
ave.rel.  vel. 


AC 


AC 


UTILIZATION  OF  KINETIC  ENERGY  IN  STEAM.     37 

The  point  corresponding  to  C  on  the  trajectory  would  then  lie 
on  its  path  a  distance  forward 

AC 


A  succession  of  points,  as  before,  will  determine  the  complete 
trajectory. 

Below  are  given  the  trajectories  for  a  blade  of  the  De  Laval 

form,  for  values  of      =  .  35,  .  4,  .  45,  .  5,  .  55,  and  .  6,  and  a  fric- 
tional  loss  of  .  08. 


FIG.  24. — Trajectory  curves. 

The  cross  section  of  the  passage  between  the  vanes  should  be  as 
nearly  uniform  as  possible.  Where  the  steam  fills  the  passage  and 
the  backs  of  the  blades  differ  in  form  from  the  faces,  there  maybe 
a  marked  difference  in  the  trajectories  of  steam  particles,  which 
means  eddies  and  inevitable  loss  of  energy. 

Fig.  25  shows  a  difference  in  the  paths  of  particles  mov- 
ing along  the  fronts  and  backs  of  the  blades,  which  is  to  be 


38  STEAM  TURBINES. 

guarded  against  as  far  as  possible  in  designing  turbine  blades. 
In  impulse  turbines  the  expansion  occurs  in  the  nozzles  or  fixed 
vanes  and  there  is  no  drop  in  pressure  as  the  steam  goes  through 
the  buckets.  This  renders  the  determination1  of  the  trajectory 
easy,  but  in  reaction  turbines  the  moving  passages  are  themselves 
nozzles,  and  the  steam  velocity  increases  sharply  in  passing 
through  them.  The  determination  of  the  trajectory  under  these 
conditions  becomes  very  involved.  Approximations  have  been 


Trajectory  for  Trajectory  for 

backatoc.  face  adc. 

FIG.  25. — Trajectory  at  front  and  back  of  blade. 

made  by  assuming  that  the  relative  velocity  increases  in  some 
regular  manner.  Having  made  some  such  assumptions  trajec- 
tories may  be  plotted  by  the  method  outlined,  but  as  they  are  at 
best  guess  work  and  of  necessity  differ  throughout  the  entire 
length  of  the  rotor  they  are  of  little  value.  The  methods  out- 
lined above  of  course  apply  to  the  Pelton  type  of  bucket  as  well 
as  to  the  side  entrance  type. 

Problems. 

1.  With  a  steam  velocity  of  2200  and  a  blade  velocity  of  800  ft.  per 
sec.  and  semicircular  blade  as  in  Fig.  23,  how  far  will  the  blade 
travel  during  the  passage  of  the  steam,  assuming  no  friction  loss? 

2.  Given  nozzle  and  blade  velocities  of  3300  ft.  and  1200  ft.  per  sec.,  a 
nozzle  angle  of  20°,  a  blade  pitch  of  5/8  in.  and  a  width  of  1  in., 
how  far  has  the  blade  moved  when  the  steam  crosses  the  center  line, 
and  how  far  at  exit? 


UTILIZATION  OF  KINETIC  ENERGY  IN  STEAM.     39 

3.  Assuming  the  W  and  blade  face  of  Prob.  2,  plot  the  trajectory  for 
u  =  .3,  .4,  and  .5  of  W. 

4.  Given  V  =3400  ft.  and  u  =1220  ft.  per  sec.,  a  =20°  and  a  pitch  of 
3/4  in.,  draw  a  section  of  the  blading  and  plot  the  trajectories  of 
the   steam   moving   along   the   face   and  back  of  the  blade  (see 
Fig.  25). 

References. 

JUDE:     "Theory  of  the  Steam  Turbine." 
STODOLA:     "The  Steam  Turbine." 


CHAPTER  III. 
CALCULATIONS  OF  TURBINE  BLADING. 

Art.  ii. — Single-stage  Impulse  Turbines. 

The  simplest  form  of  successful  turbine  is  the  single-stage 
impulse  turbine.  In  this  all  the  expansion  occurs  in  one  set  of 
nozzles,  where  the  heat  energy  availablejs  converted  into  kinetic 
energy  and  directed  against  a  single  row  of  moving  vanes. 

As  the  steam  velocity  varies  with  the  heat  drop  and  the  vane 
velocity  with  that  of  the  incoming  steam,  the  speed  of  the  rotat- 
ing vanes  in  the  case  of  single  expansion  is  very  high,  from  1,000 
to  1,400  feet  per  second,  or  about  half  the  velocity  of  a  modern 
high  powered  rifle  bullet.  De  Laval  frankly  accepted  these  speeds 
and  developed  a  machine  capable  of  withstanding  the  strains 
produced.  Some  idea  of  the  problems  involved  may  be  had 
from  the  fact  that  in  the  300-horse-power  turbines  the  blades, 
weighing  only  1/28  of  a  pound  each,  but  running  with  a  velocity 
of  1380  feet  per  second  on  a  15-inch  radius,  develop  a  centrifugal 
force  of  3/4  of  a  ton.  It  called  for  engineering  ability  of  a  high 
order,  and  greatest  care  in  the  details  of  design  and  manufac- 
ture, for  not  only  was  a  built  up  rotor  required  capable  of  running 
from  10,000  to  30,000  R.P.M.,  according  to  the  size,  but  the 
velocities  developed  had  to  be  reduced  through  gearing  to  ones 
which  could  be  used.  An  efficient  and  practical  machine  has 
been  developed,  however,  which  runs  with  gear  velocities  of  100 
feet  per  second  with  but  little  wear,  no  vibration,  and  high 
efficiency. 

The  relation  between  the  pressures  and  velocities  during  the 
passage  of  the  steam  through  an  impulse  turbine  of  the  De  Laval 
type  is  shown  schematically  in  Fig.  26.  The  boiler  pressure 
drops  in  a  single  expansion  to  the  exhaust  pressure  before  the 
steam  enters  the  vanes.  The  wheel  therefore  has  equal  pressure 
on  both  sides.  The  velocity  V  of  the  steam  is  maximum  as  it 
enters  the  vanes  and  is  nearly  all  absorbed  in  the  passage  through 

40 


CALCULATIONS  OF  TURBINE  BLADING. 


41 


them.     The  steam  enters  the  exhaust  chamber  with  the  low 
velocity  v,  sufficient  only  to  clear  the  wheel. 

As  an  example  of  calculation  for  the  blading  of  a  turbine  of 
this  type  let  the  jsteam  conditions  be  the  same  as  for  the  example 
on  page  22,  namely, 


Initial  steam  pressure, 
Initial  dryness 
Final  steam  pressure 


150  pounds  gauge 
981/2  % 
1  pound  absolute 


Boiler  Pressure 


Velocity  in 
Steam  Pipe 


Exhaust 
chamber 


Condenser  Pressure" 


Fia.  26. — Scheme  of  single  stage  impulse  turbine. 


In  addition  let  the 
Output 

Revolutions  per  minute  of  wheel  = 
Blade  velocity  be  limited  to 
Number  of  nozzles 
Angle  of  nozzles 


110  H.  P. 
13000 
1250  feet  per  second 

6 
20° 


Angle  of  entrance  and  exit  of  blades  to  be  equal. 

As  already  pointed  out  in  Art.  8  the  design  of  the  blading, 
and  in  fact  of  the  whole  turbine,  is  materially  affected  by  the 
frictional  losses  in  the  nozzles  and  blades.  In  determining  the 
proportions  for  a  given  case  assumptions  must  be  made  for  these, 
based  on  experience.  Stodola  gives  the  following  values  for  the 
various  losses.1 

1  Steam  Turbines,  2nd  ed.,  p.  224. 


42 


STEAM  TURBINES. 


Losses  in  the  nozzle 
Losses  in  the  blades 
Losses  at  exit 
Total  loss 


=  15%  of  the  available  energy 
=  21%  of  the  available  energy 
=   4.6%  of  the- available  energy 
=  40.6%  of  the  available  energy 


From  the  given  conditions  of  steam  and  exhaust  the  theoretical 
heat  drop  available  is  319  B.  T.  U.  But  assuming  a  nozzle  loss  of 
15%,  only  319X- 85  =  271  B.  T.  U.  will  be  transformed  into 
kinetic  energy.  From  Eq.  (6)  we  have  7  =  223.8^/271  = 
3680  feet  per  second.  (See  problem  in  Art.  7.) 

3680  X   94 
From    Eq.   (21)  u= =1730    feet    per    second    for 

maximum  efficiency.  For  mechanical  reasons  u  will  be  limited 
to  1250  feet  per  second  as  given  in  the  initial  conditions.  The 


FIG.  27. — Velocity  diagram. 


21 
energy  loss  in  the  blades  is  21%  of  the  total,  or  '-    =24.7%  of 

.85 

that  delivered  to  the  blades  by  the  nozzles.  If  2540  feet  per 
second  be  the  relative  velocity  at  entrance,  as  shown  by  the 
velocity  diagram,  Fig.  27,  the  relative  velocity  at  exit  will  be 
such  that  the  kinetic  energy  is  24  .  7  %  less,  or 


25402  W* 

—  x.753=  -1-.     Hence 


Wl  =  A/25402  X  .753  =  2200  feet  per  second. 

The  diagram  shows  that  the  blade  angles  are  30°  and  the  final 
velocity  F1  =  1280  feet  per  second.     Comparison  of  Fig.  27  with 


CALCULATIONS  OF  TURBINE  BLADING.  43 

Figs.  19  and  20  shows  how  friction  and  mechanical  limitations 
modify  the  theoretical  conditions. 

Comparing  reported  tests  of  similar  turbines,  18  pounds  per 
B.  H.  P.  hour  may  be  assumed  for  the.  steam  rate  on  which  to  .base 

1 8  V  1 1 0 
the  nozzle  areas.     Then =  .55  pounds  of  steam  must  be 

oOUU 

delivered  per  second  by  the  six  nozzles  or  .  092  pounds  for  each 
nozzle.  The  proportions  of  a  nozzle  for  these  conditions  have 
already  been  worked  out  in  Art.  7  and  are  shown  in  Fig.  11. 
13000  R.  P.  M.  have  been  assumed  for  the  rotor  shaft,  and  1250 

feet  per  second  for  u,  therefore  —  -  -  =  5 . 75   feet  is  the  cir- 

loUUU 

cumference  of  the  blade  circle,  which  corresponds  to  a  pitch 
diameter  of  22  inches.  From  Art.  8  the  pitch  may  be  assumed 
as  approximately  5/8  inch,  which  gives  us  110  blades.  Since 
the  exit  diameter  of  the  nozzle,  Fig.  11,  is  .99  inches  we  may 
make  the  blades,  say,  11/8  inches  high. 

Problems. 

-A i.  Given  the  steam  conditions  of  Prob.  1.,  Art.  7,  namely: 

Steam  pressure  =120  Ibs.  gauge. 

Superheat  =  40°  F. 

Exhaust  at  atmospheric  pressure 

Output  =  100  K.  W. 

R.  P.  M.  of  wheel  =12000. 

Blade  velocity  =  1200  ft.  per  sec. 

Number  of  nozzles  =8. 

Angle  of  nozzles  =20°. 

Blades  symmetrical. 

Design  nozzles  and  blading  for  a  single  stage  impulse  turbine 
assuming  a  steam  rate  of  50  Ibs.  of  steam  per  K.  W.  hr. 

2.  Design  nozzles  and  blading  for  a  condensing  turbine,  conditions  as 
in   Prob.  1,  except  exhaust    pressure  =1.5  Ibs.  absolute.     What 
changes  of  design  are  involved  ?  Assume  a  steam  rate  of  26  Ibs.  per 
K.  W.  hr. 

3.  Design  nozzles  and  blading  for  a   single  stage  impulse  turbine. 
Steam  pressure  15  Ibs.  absolute;  exhaust  pressure  1  Ib.  absolute; 
quality  of  steam  at  admission  =  88%;  blade  velocity  =  1200  ft. 
per  sec.     Take  steam  rate  at  42  Ibs.  per  K.  W.  hr. 

4.  Report  on  the  construction  and  efficiency  of  the  reduction  gearing 
of  the  DeLaval  steam  turbine. 


44 


STEAM  TURBINES. 
References. 


STODOLA:     " The  Steam  Turbine." 
NEILSON:     "The  Steam  Turbine." 
THOMAS:     " Steam  Turbines." 
LEA  AND  MEDEN:    Paper,  "DeLa- 
vol.  xxv. 


Steam  Turbines,"  A.  S.  M.  E. 


Art.  12.— Multi-stage  Impulse  Turbines. 

As  seen  in  the  last  article  a  single-stage  impulse  turbine  must 
run  at  a  very  high  velocity  and  be  geared  down. 

There  are  two  ways  by  which  the  velocity  of  an  impulse  tur- 
bine may  be  reduced,  by  subdividing  the  heat  drop  in  a  series  of 


FIG.  28. — Scheme  of  impulse  turbine  with  single  pressure  stage 
and  several  velocity  stages. 

expansions,  and  by  having  the  steam  impinge  on  two  or  more  rows 
of  buckets  after  expansion.  The  shaft  velocity  can  thus  be 
reduced  to  a  point  where  the  turbine  can  be  directly  connected 
to  a  generator,  blower,  or  centrifugal  pump.  Such  turbines  are 
more  complex  and  theoretically  less  efficient  than  the  single- 
stage  machine.  This  is  offset,  however,  by  the  advantages  of 
direct  connection  and  lower  speed.  The  De  Laval  type  of  single- 


CALCULATIONS  OF  TURBINE  BLADING. 


45 


stage  turbine  finds  its  limit  at  about  500  H.  P.  Beyond  this 
the  strains  become  too  great  and  the  problem  of  speed  reduction 
too  troublesome.  In  the  multi-stage  type,  however,  there  seems 
to  be  almost  no  limitation  of  the  power  which  can  be  developed 
by  a  single  machine.  Curtis  turbines  of  this  type  are  in  use 
developing  20,000  K.  W.,  and  larger  units  might  be  used  were 
they  commercially  desirable. 

The  field  of  the  multi-stage  turbine  is  much  wider  than  that  of 
the  single-stage,  and  it  constitutes  the  second  of  the  main  divisions 
into  which  turbines  may  be  separated. 

Fig.  28  illustrates  the  action  of  the  original  Curtis  and  the 
Riedler  turbines.  Complete  expansion  occurs  as  before  in  a 


Fia.  29. — Scheme  of  Curtis  turbine,  multi-pressure,  multi-velocity  stage. 

single  set  of  nozzles,  and  the  steam  enters  the  first  row  of  blades 
at  high  velocity  as  in  the  previous  case.  The  steam  leaves  this 
row,  however,  with  considerable  velocity,  is  redirected  by  a  set  of 
stationary  guide  vanes  and  impinges  on  the  next  row,  and  so  on 
to  the  exhaust  chamber.  The  drops  in  steam  velocity  occur  in 
the  passage  through  the  moving  blades.  The  stationary  vanes 
are  merely  guides,  and  the  velocity  during  the  passage  through 
them  is  substantially  constant,  as  shown.  The  increase  of 
length  in  the  successive  rows  of  stationary  blades  is  to  allow 
for  the  decrease  in  velocity,  not  for  increase  in  volume.  Theo- 
retically the  exhaust  pressure  with  its  corresponding  volume  is 
reached  at  the  nozzle,  and  all  the  rows  of  blades  are  driven  by 


46  STEAM  TURBINES. 

kinetic  energy,  revolve  in  a  vacuum  with  the  least  possible  resist- 
ance, and  the  wheels  are  balanced  for  pressures.  This  is  a  single- 
pressure,  multi-velocity  stage  type  and  is  still  used  on  the  smaller 
Curtis  turbines  up  to  about  35  K.W. 

As  now  built  the  Curtis  turbines  have  the  pressure  drop  divided 
into  two  or  more  "  pressure  stages."  Steam  is  partially  expanded 
in  a  set  of  nozzles  to  some  lower  pressure  and  passes  through  a  num- 
ber of  rows  of  moving  blades  as  at  a,  Fig.  29,  constituting  one 
stage  where  its  kinetic  energy  is  absorbed.  It  is  then  expanded 
again  and  goes  through  another  series  of  blades,  or  second  stage,  b. 
The  number  of  stages  and  of  rows  in  each  stage  varies  with  the 


FIG.  30. — Scheme  of  multicellular  turbine,  multi-pressure,  single- velocity  stage. 


conditions.  As  before,  the  wheels  are  balanced,  and  there  is  no 
end  thrust.  The  pressure  throughout  each  stage  is  constant,  the 
drops  occurring  in  the  expanding  nozzles  at  the  begin- 
ning of  each  stage.  This  may  be  described  as  a  multi-pressure, 
multi-velocity  stage  machine. 

This  idea  of  breaking  up  the  pressure  drop  is  carried  to  the 
limit  in  the  "multi-cellular"  turbines,  Fig.  30,  such  as  the 
Rateau,  Zoelly,  Kerr,  and  Wilkinson  machines.  Here  a  set  of  ex- 
pansion nozzles  after  each  row  of  blades  replaces  the  fixed 
guide  vanes,  and  accelerates  the  steam  to  a  certain  velocity, 
which  is  absorbed  in  the  following  running  wheel.  The  multi- 
cellular  turbine  is  therefore  a  multi-pressure,  single-velocity 
tage  machine.  A  turbine  has  been  patented1  which  is  similar 
to  Fig.  30  except  that,  while  the  velocity  drop  is  about  as  usual, 

'U.  S.  Patent,  J.  F.  M.  Patitz,  Oct.  4,  1910. 


CALCULATIONS  OF  TURBINE  BLADING. 


47 


both  velocities  V  andFj  are  high  i.e.,  the  broken  line  in  Fig.  30 
is  raised  as  a  whole.  The  energy  available  in  a  single  stage 
varies  with  V2—  V ^,  and  is  much  greater  for  a  given  drop  when 
both  velocities  are  high.  It  is  hoped  by  this  means  to  reduce 
greatly  the  number  of  stages,  but  this  will  be  partially  offset  by 
greater  steam  friction.  See  Probs.  3  and  4,  p.  3. 

In  all  of  these  forms  there  will  be  noticed  the  characteristic 
which  defines  impulse  turbines,  that  there  is  no  fall  of  pressure  in 
the  moving  blades.  Expansion  occurs  only  in  fixed  passages  or 
nozzles,  and  the  moving  blades  are  free  from  end  thrust. 


FIG.  31. — Velocity  diagram  for  two  stages. 

The  determination  of  the  velocities  in  the  multi- velocity  stage 
turbine  is  an  extension  of  the  method  already  outlined.  The  final 
velocity,  Vlt  at  exit  from  the  first  row,  Fig.  31,  is  deflected  and 
becomes  the  initial  velocity  for  the  second  row  of  blades,  and  so 
on  for  the  whole  number  of  rows.  When  the  rows  of  buckets 
have  the  same  mean  diameter,  as  is  usual,  u  has  the  same  value 
for  each  row.  The  diagram  may  be  arranged  conveniently  and 
more  compactly  by  extending  the  line  of  the  vane  velocity  as  in 
Fig.  32,  and  laying  off  a  succession  of  lengths,  each  equal  to  u, 
and  connecting  each  with  the  point  a,  as  shown.  With  an  initial 
velocity  of  2430  feet  per  second,  a  blade  velocity  of  400  feet  per 
second,  and  a  nozzle  angle  of  22  1/2°,  the  exit  velocity  from 
the  second  row  of  moving  blades  is  1130  feet  per  second,  and  the 


48  STEAM  TURBINES. 

blade  angle  42°.  Proper  allowance  for  friction,  however, 
materially  affects  the  design  and  should,  as  before,  be  taken  into 
account.  Fig.  33  shows  how  this  may  be  done,  and  gives  the 
diagram  where  friction  in  the  entering  nozzle  has  reduced  the 
velocity,  V,  to  2320  feet  per  second,  and  in  each  succeeding  row 
a  friction  loss  of  10%  is  assumed.  Comparison  of  the  blade  sec- 
tion as  determined  by  the  two  diagrams  shows  a  marked  differ- 
ence. If  the  radii  of  the  successive  rows  on  the  shaft  are  not 


FIG.  32. — Velocity  diagram  for  Curtis  turbine,  no  allowance  for  steam  friction. 

equal,  the  length  of  u  should  be  made  to  increase  directly  as  the 
diameter.  In  general,  the  friction  loss  is  not  constant  through  the 
successive  stages,  but  increases  from  3%  or  4%  to  perhaps  10% 
with  increasing  presence  of  water  in  the  steam.  Proper  values  can 
be  assigned  only  from  experience.  The  method  of  finding  the 
velocities  in  Fig.  33  is  applicable  for  an  increasing  friction  loss 
as  well  as  for  a  constant  one. 

As  an  illustration  of  calculations  for  blading  in  a  multi-stage 
impulse  turbine,  let  the  following  conditions  be  given: 


CALCULATIONS  OF  TURBINE  BLADING. 


49 


Initial  steam  pressure 

Initial  superheat 

Final  pressure 

Assume  a  blade  velocity  u 

Assume  nozzle  angles 


=  175  pounds  absolute 
=  140°Fahr. 
=      1  pound  absolute 
=  400  feet  per  second 
=   22  1/2° 


Assume  10%  energy  loss  in  the  nozzles  and  10%  velocity 
loss  in  each  row  of  vanes.  Let  the  turbine  be  of  the  Curtis  type 
with  three  stages  and  two  rows  of  moving  blades  in  each  stage. 


FIG.  33. — Velocity  diagram  for  Curtis  turbine  with  allowance  for  steam  "friction. 

For  convenience  part  of  the  heat  chart  is  reproduced  in  Fig. 
34.  The  initial  condition  of  the  steam  is  given  by  the  intersection 
of  the  175-pound  pressure  line  and  the  140°  superheat  line.  A 
vertical  line  dropped  to  the  1  pound  line  gives  357  B.  T.  U.  as  the 
total  heat  drop  for  pure  adiabatic  expansion.  Dividing  this 
drop  as  nearly  equally  as  possible  at  AC,  CD,  and  DB,  we  have 
the  pressure  ranges  for  the  first  three  stages. 

First,  175  pounds  to  45  pounds  absolute. 
Second,  45  pounds  to  8  pounds  absolute. 
Third,  8  pounds  to  1  pound  absolute. 


50 


STEAM  TURBINES. 


Deducting  CC'  =  10%  of  AC  for  the  assumed  heat  loss  in  the  ex- 
panding nozzle,  we  have  AC',  which,  referred  to  the  velocity 
scale,  gives  2320  feet  per  second  initial  velocity.  As  u  and  a 
are  given,  we  may  draw  the  velocity  diagram,  allowing  for  the 
10%  velocity  loss  in  each  row.  This  is  given  in  Fig.  33,  where 


FIG.  34. — Condition  curve,  Curtis  turbine. 

the  final  velocity  is  found  to  be  673  feet  per  second.     The  blade 
sections  thus  determined  are  given  in  the  same  figure. 

From  Eq.  (3.)  the  force  per  pound  of  steam  acting  in  the  line 

W 
of  motion,  due  to  entrance,  is        V  cos  a  and  that  due  to  the 

.    TP,  ' 

exit  is  — -  F/  cos  /?'.    Remembering  that   W  here  is  unity  the 

total   force    acting    on   the   first    row  per    pound  of  steam  is 


CALCULATIONS  OF  TURBINE  BLADING.  51 


-  and  the  work  done  is  this  expression  multi- 

plied by  the  blade  velocity,  u,  or  the 

Work  done  in  the  first  row  per  second.  per  pound  of  steam  = 

U-  (Vcosa-Vicosp).  (26) 

9 

A  similar  expression  gives  the  work  done  in  the  second  row  of 
moving  blades.  The  velocities  required  may  be  scaled  from  the 
velocity  diagrams. 

The  actual  energy  per  pound  of  steam  which  has  gone  into  work 
during  passage  through  the  stage  is  thus  found  to  be  56540 
foot-pounds  or  in  its  heat  equivalent,  72.8  B.T.U.  This  is  laid 
off  on  the  heat  drop  at  AE  in  Fig.  34  and  the  remainder  EC,  in 
this  case  about  40%  of  AC,  is  still  in  the  steam  as  heat  energy. 
Since  the  steam  is  now  at  a  pressure  of  45  pounds  absolute, 
and  has  a  total  heat  corresponding  to  the  ordinate  of  E,  the  con- 
dition of  the  steam  at  the  beginning  of  the  second  stage  is  found 
by  projecting  E  horizontally  until  it  meets  the  45  pound  line  as 
at  F.  From  the  position  of  F  it  is  seen  that  the  steam,  instead  of 
being  98%  quality,  is  superheated  about  GO9  Fahr.  Dropping 
a  vertical  from  F  to  the  8  pound  line  shows  an  adiabatic  heat 
drop  of  126  B.  T.  U.,  which,  with  10%  allowance  for  losses,  gives 
a  velocity  of  2380  feet  per  second.  Laying  out  the  diagram  as 
before,  we  have  an  exit  velocity  of  710  feet  for  the  second  stage. 
The  work  for  this  stage  is  found,  by  the  previous  method,  to  be 
59,150  foot-pounds  per  pound  of  steam,  and  the  corresponding 
actual  heat  drop,  76  B.  T.  U.  Applying  this  to  the  heat  chart  as 
before,  we  find  that  the  steam  enters  the.  third  or  last  stage  with 
a  quality  of  .986.  The  adiabatic  heat  drop  for  the  last  stage  is 
129  B.  T.  U.,  and  the  velocity,  allowing  far  losses,  is  2400  feet 
per  second.  The  energy  developed  in  this  stage  is  59,600  foot- 
pounds per  pound,  and  the  corresponding  heat  drop,  76  .  7  B.  T.  U. 
From  this  last  we  can  obtain  the  final  condition  of  the  steam  at 
/,  where  it  is  found  to  have  a  dryness  of  .947%. 

Adding  the  work  of  the  three  stages,  we  have 
First  stage  .................  .....       56,540 

Second  stage  ....................       59,150 

Third  stage  .....................       59,600 

Total  work  per  pound  of  steam  =      175,290 


52 


STEAM  TURBINES. 


CALCULATIONS  OF  TURBINE  BLADING.  53 

1,980,000 

The    theoretical    steam    rate  = — =  11.3    pounds    per 

175,290 

H.  P.  hour.     Allowing  8%  for  mechanical  friction,  windage,  etc., 

11  3 

this  becomes  —  '—  =12.3  pounds. 
.  92 

If  the  generator  efficiency  be  taken  at  95%  we  have  a  steam 
rate  of  13  pounds  per  E.  H.  P.  hour,  or  17.5  pounds  per  K.  W. 
hour,  on  the  basis  of  a  power  factor  of  unity. 

As  in  Fig.  12,  a  quality  curve  may  be  drawn  through  the 
points  A,  F,  H,  and  I,  which  will  give  the  condition  of  the  steam 
for  any  point  during  the  expansion.  With  this  determined,  and 
with  the  H.  P.  to  be  developed,  and  the  steam  rate  as  found  above, 
we  have  the  basis  for  the  calculation  of  the  lengths  of  the  blades. 

Problems. 

1.  Make  diagrams  and  calculations  for  a  Curtiss  turbine  with  5  pres- 
sure stages,  each  of  2  velocity  stages. 

Initial  steam  pressure  =  155  Ibs.  abs. 

Superheat  =75°  F. 

Final  pressure  =28  in.  vac. 

Assumed  blade  velocity  =425  ft.  per.  sec. 

Nozzle  angle  =22°. 

Velocity  loss  in  each  nozzle  5%. 

Velocity  loss  in  each  row  of  blades         10%. 

Calculate  the  nozzle  area  and  blading  for  a  500  K.  W.  turbine,  the 
mechanical  and  generator  friction  being  taken  at  the  values  given 
on  p.  117. 

2.  Make  diagrams  and  calculations  for  a  L.  P.  Curtis  turbine,  the  con- 
ditions being  those  of  Prob.  1,  except  that  the  initial  pressure  is 
15  Ibs.  absolute  and  there  are  two  pressure  stages,  each  with  two 
velocity  stages.     The  nozzle  angles  to  be  25°. 

3.  Report  on  the  Small  Curtis  Turbine.     See  paper  of  G.  A.  Orrok, 
Trans.  A.  S.  M.  E.,  vol.  xxxi,  p.  263. 

4.  Report  on  a  Comparison  of  the  Rateau  or  multicellular,  and  the 
Curtis  Principles  of  Design.    Power,  Dec.  20,  1910,  p.  2218,  and 
Jan.  3  and  10,  1911,  pp.  19  and  64. 

References. 

STODOLA:     "  The  Steam  Turbine." 
THOMAS:     " Steam  Turbines." 
EMMET:     "The  Steam  Turbine  in  Modern  Engineering,"  Trans.  A.  S. 

M.  E.,  vol.  xxv. 
See  also  references  in  the  problems. 


54  STEAM  TURBINES. 

Art.  13.— Single  Flow  Impulse -reaction  Turbine. 

An  impulse  turbine  as  indicated  in  Art.  12  is  one  in  which 
expansion  occurs  only  in  the  fixed  passages  or  nozzles. 

A  reaction  turbine  is  one  in  which  the  energy  is  derived  from 
the  reaction  of  steam  issuing  from  openings  or  nozzles  in  the  mov- 
ing wheel.  No  pure  reaction  turbine  is  being  built  at  this  time. 
A  number  were  built  in  this  country  many  years  ago  by  Avery, 
but  they  have  long  since  been  abandoned.  Theoretically,  there 
is  no  reason  why  a  pure  reaction  turbine  might  not  be  built,  but 
the  velocities  involved  are  so  high  as  to  render  the  type  impracti- 


B oiler  Press. 


I 


Velocity 


FIG.  36. — Scheme  of  impulse- reaction  turbine. 

cal.  A  combination  of  the  impulse  and  reaction  principles  has, 
however,  led  to  one  of  the  largest  and  most  important  types  of 
turbines  yet  developed. 

Figs.  55  and  67  show  sectional  elevations  of  two  Parsons  or 
impulse-reaction  turbines,  both  single-flow,  i.e.,  the  steam 
enters  at  the  end  and  flows  axially  in  one  direction.  Fig.  36, 
corresponding  to  Figs.  23  to  26,  illustrates  their  operation. 
The  general  form  of  the  buckets  is  shown  in  Fig.  37,  in  which  it 
is  seen  that  the  curve  at  the  entering  end  of  the  moving  vane  acts 
as  in  impulse  turbines,  to  absorb  the  kinetic  energy  discharged 
from  the  fixed  nozzles.  The  long  straight  portion  at  the  exit 
end  of  the  moving  blades  forms  a  nozzle  which  restores  the 
velocity  just  absorbed  and  adds  the  power  of  the  reaction  of 
exit  to  that  of  the  impulse  first  received.  In  this  type  there  is 
an  almost  uninterrupted  lowering  of  the  pressure.  If  there  were 


CALCULATIONS  OF  TURBINE  BLADING. 


55 


Moving  blades 


no  motion  in  the  rotor  there  would  be  a  corresponding  rise  in  the 
steam  velocity,  as  shown  in  the  curved  line,  Fig.  36.  In  fact,  the 
long  passage  between  the  rotor  and  the  casing  is  essentially  an 
enlarged  nozzle,  its  sectional  area  increasing  steadily,  and  con- 
forming roughly  to  that  which  would  be  given  an  expanding 
nozzle. 

The  impulse-reaction  turbine  allows  the  lowest  velocities  which 
have  been  attained  with  high  economy.  Its  construction  is 
much  more  complicated  than 
the  simple  De  Laval  wheel,  but 
it  has  been  successful  in  a  very 
wide  range  of  service. 

In  the  impulse-reaction  dia- 
gram, Fig.  37,  the  fixed  vanes 
beyond  the  first  row  of  moving 
blades  receive  the  steam  at  a 
velocity,  V1}  using  the  same 
notation  as  on  page  29.  The 
steam,  in  passing  through  the 
fixed  vanes,  expands,  and  the 
velocity  increases  to  V.  With 
respect  to  the  following  row  of 
moving  blades,  the  steam  enters  at  the  velocity  W.  In  passage 
through  the  moving  blades  there  is  further  expansion,  and  the 
steam  leaves  them  at  a  high  velocity,  Wv  The  total  work  done 


Fixed  Vanes 


in  the  moving  blades  is :   First,  the  energy 


29 


per     pound 


of  steam  produced  in  the  guide  blades  and  expended  upon 
the  moving  vanes;  second,  the  reaction  accompanying  the 
increase  of  steam  velocity  in  the  moving  blade  from  W  to 


Wlf  which  is  equal  to  —  - 


per  pound  of  steam  used.     The 


guide  blades  and  moving  vanes  usually  have  the  same  form  and 
angles,  consequently  these  two  expressions  are  equal,  and  the 
total  work  is  divided  equally  between  impulse  and  reaction. 
This  type  of  turbine  is  subject  to  end  thrust  which  is  balanced 
by  pistons  on  the  rotor  as  shown  in  Figs.  55  and  67. 

Before  the  vanes  can  be  designed  in  this  type,  the  heat  drop 
in  the  various  stages  must  be  determined,  and  for  this  the  follow- 
ing data  and  assumptions  are  required: 


56 


STEAM  TURBINES. 


1.  The  initial  steam  pressure,  with  dryness  or  superheat. 

2.  The  exhaust  pressure. 

3.  The  absolute  velocity,  V,  of  steam  as  it  leaves  guide  blades. 
This  varies  progressively  through  the  turbine. 

4.  Friction  losses  of  the  steam  in  passing  through  the  turbine. 

5.  The  exit  angles  of  fixed  and  moving  blades. 

6.  The  peripheral  velocity  of  the  blades  for  the  various  cylin- 
ders or  steps. 

The  exit  angles  are  made  the  same  for  both  guide  vanes  and 
rotating  blades,  ordinarily  between  20°  and  30°.  The  smaller 
angles  than  these,  while  apparently  increasing  the  power,  lead 
to  contracted  passages  and  increased  friction.  On  the  other 
hand,  with  too  great  angles  the  power  for  each  stage  decreases, 
requiring  too  many  stages,  and  increasing  the  size  of  the  turbine. 
The  peripheral  velocity  u  (item  6  above)  at  the  H.  P.  stage 
varies  from  100  to  135  feet  per  second  and  increases  as  the  size  of 
the  rotor  increases  in  the  later  stages.  Table  I,  from  a  paper 
of  E.  M.  Speakman,  gives  some  basis  for  selecting  the  vane 
velocities. 


Table  I. 

PARSONS  TURBINE  PRACTICE. 
Electrical  Work. 


Peripheral  Vane  Speed 

Rated  Capacity 

Number  of 
Rows 

Revolutions 
Per  Minute 

First 

Last 

Expansion 

Expansion 

5000    K.  W. 

135 

330 

70 

750 

3500     K.  W. 

138 

280 

75 

1200 

2500     K.  W. 

125 

300 

84 

1360 

1500     K.  W. 

125 

360 

72 

1500 

1000     K.  W. 

125 

250 

80 

1800 

750     K.  W. 

125 

260 

77 

2000 

500     K.  W. 

120 

285 

60 

3000 

250     K.  W. 

100 

210 

72 

3000 

75     K.  W. 

100 

200 

48 

4000 

CALCULATIONS  OF  TURBINE  BLADING. 

Marine  Work. 


57 


Type  of  Vessel 

Peripheral  Vane  Speed 

Mean 
Ratio  of  ^ 

No.  of 

Shafts 

In  H.  P. 

In  L.  P. 

High  speed  mail  steamer 
Intermediate  mail  steamer 
Channel  steamers  

70-80 
80-90 
90-105 
85-100 
105-120 
110-130 

110-130 
110-135 
120-150 
115-135 
130-160 
160-210 

.45-.  5 
.47-.  5 
.37-.  47 
.48-.  52 
.47-.  5 
.47-.  51 

4 
3  or  4 
3 
4 
3  or  4 
3  or  4 

Battleships  and  cruisers. 
Small  cruisers  
Torpedo  craft  

The  steam  velocity  (item  3)  varies  from  2  to  3.5  times  the 
blade  velocities.  When  it  would  rise  above  this  in  the  pro- 
gressive expansion  along  the  rotor,  the  diameter  of  the  rotor  is 
increased,  beginning  a  new  step  or  drum. 

The  heat  drop  in  any  stage  (i.e.,  one  row  of  fixed  vanes  and  one 
row  of  moving  blades)  may  be  found  readily  by  the  following 


.Example  of  calculation  for  "Stage  Dropj'-First  Stage  A 
Aa=Aa  below  =V=  200 'per  sec. 
Ab=Ab      ••      =n=120' "     " 
In  diagram  bf  =170,  by  scaling 


FIG.  38.- — Velocity  curves  and  heat  drops,  single  flow  impulse-reaction  turbine. 

simple  graphical  construction,  Fig.  38.  In  the  velocity  tri- 
angle formed  by  V,  W,  and  u,  produce  u  and  drop  a  perpendic- 
ular aa'  upon  it  from  a.  With  a',  the  base  of  this  perpendicular, 
as  a  center,  and  Aaf  as  a  radius,  describe  the  arc  afp.  Drop  a 


58  STEAM  TURBINES. 

perpendicular  from  b,  cutting  the  arc  at  /.     The  work  done  in  foot- 
pounds per  pound  of  steam  in  the  stage  is    W  —  —  •    ,  where  bfis 

y 
measured  to  the  same  velocity  scale  as  u  and  Vr 

The  proof  of  this  is  as  follows: 

The  separate  velocity  diagrams  in  Fig.  33  may  be  combined 
as  shown,  and  where  the  work  is  divided  equally  between  impulse 
and  reaction  the  figures  will  be  symmetrical  with  respect  to  aa'. 
The  velocities  of  exit  from  the  fixed  and  moving  blades  are  W 
and  Vi,  and  from  Eq.  (26)  the  work  is  done 

u(V cosa+ViCos  /3)  u(Aa'+a'o) 


But  bf,  being  the  perpendicular  from  /to  the  hypothenuse  of  the 
right-angled  triangle  a,  f,  p,  inscribed  in  a  semicircle,  is  the  mean 
proportional  between  the  segments  ab  and  bp,  therefore 

bf2  —  AbXbp  and  since  bp  =  ao, 
=  Ab(Aa'-\-a'o) 
=  u(V  cos  a+V^os  $ 


9 
The  heat  drop  producing  the  work  will  be 


-mfa      (-m)  • 

If  the  heat  drops  in  the  various  stages  were  equal,  the  number 
of  stages  could  be  determined  at  once  by  dividing  the  total  heat 
drop  from  inlet  to  condenser  by  the  stage  drop  assumed.  The 
stage  drops,  however,  vary,  those  nearest  the  condenser  being 
much  greater  than  the  earlier  ones.  A  method  of  determining 
these,  outlined  by  Prof.  Stodola,  will  be  used  in  working  out  a 
definite  case.  The  conditions  will  be  taken  as  follows: 

Normal  capacity  =2000  K.  W. 

Overload  capacity,  without  by-pass,  =2400  K.  W. 

Initial  pressure  =  175  pounds  absolute 

Superheat  = 50° 

Condenser  pressure  =  l  pound  absolute 


CALCULATIONS  OF  TURBINE  BLADING.  59 

R.  P.  M.  =3,600 

Number  of  drums  =  4 

Loss  due  to  steam  friction  28% 

Loss  due  to  leakage  =   6% 

Loss  due  to  windage,  bearings,  etc.,  =  15% 

Energy  in  exhaust  =   3% 

Total  losses  in  addition  to  steam  friction  =  24%. 

Efficiency  of  generator  94% 

We  must  first  assume  blade  velocities.  From  reference  to 
Table  I  on  page  56  these  may  be  taken  as 

it  =  120  feet  for  first  stage,  increasing  to 
w  =  320  feet  at  exhaust  end. 

Assume  also  exit  angles  for  all  blades  and  vanes  =24°,  and  a 
clear  area  through  the  blades  =  1/3  of  the  cross  section  of  the 
opening. 

Lay  off,  as  in  the  lower  part  of  Fig.  38,  a  horizontal  base  AB 
to  represent  the  length  of  the  rotor.  Let  the  steam  velocity  in 
the  first  stage  be  200  feet  per  second,  and  in  the  final  stage  be 
950  feet,  these  values  being  based  on  experience.  The  curve 
of  steam  velocities  must  be  assumed.  It  follows  approximately 
a  hyperbolic  curve  except  toward  the  exhaust  end,  where  it 
rises  rapidly.  The  curve  here  drawn  is  about  as  followed  in 
practice. 

The  velocity  w=12Q  feet  per  second,  for  the  first  cylinder,  is 
laid  off  at  the  left,  and  the  velocity  320  feet,  for  the  last  cylinder, 
is  laid  off  at  the  right.  The  most  advantageous  ratio  between 

v 

the  steam  and  blade  velocities      is  from  2  to  3  and  it  should  vary 

u 

between  about  the  same  limits  on  each  drum.  It  is  customary 
also  to  make  the  ratio  between  the  successive  drum  diameters 
substantially  constant.  The  blade  velocities,  on  this  basis,  come 
to  120,  165,  225,  and  320  feet  per  second. 

Moyer  gives  an  empirical  formula  for  determining  the  number 
of  stages: 


(28) 


60  STEAM  TURBINES. 

where  C  is  a  constant  which  varies  from  1,500,000  for  marine  tur- 
bines to  2,600,000  for  electric  generator  service,  and  u  is  the  mean 
blade  velocity  in  feet  per  second  of  the  cylinder  considered.  The 
n  found  is  the  number  of  rows  required  if  the  blade  speed  for 
the  whole  turbine  were  u.  As  the  cylinder  considered  develops 
a  certain  fraction  only  of  the  total  power,  the  number  of  rows 
required  for  that  cylinder  will  be  that  fraction  of  the  n  found 
in  the  formula. 

It  can  be  seen  from  the  wide  range  in  the  constant  that  reliance 
on  this  formula  calls  for  experience  on  the  part  of  the  designer 
with  the  working  conditions  and  their  relation  to  the  constant 
used.  It  may  be  used  to  great  advantage  by  any  one,  however,  as 
giving  a  good  approximation  for  the  number  of  blades  on  each 
drum  or  cylinder.  Let  us  assume  that  the  power  developed  by 
the  various  cylinders  shall  be  approximately  1/6,  1/5,  1/4,  and 
3/8  of  the  total. 

Then,  taking  C  at  2,500,000,  for 

2500000 
1st  cylinder,      ^  =  —-——.1/6=30  stages 

•    2500000 

2nd  cylinder,     n2  =  -—  —  --  .1/5  =  18  stages 
loo 

2500000 

3rd  cylinder,      n3  =     00^    .1/4  =  12  stages 
22o 

2500000 
4th  cylinder,     nt  =  -—  ~—  —  .  3  /8  =   6  stages 


Total  66  stages. 

The  stages  are  spaced  off  uniformly  on  AB  and  the  drum  lengths 
located  tentatively  as  at  cd,  ef,  and  gh. 

The  heat  drop  which  would  occur  in  a  stage  located  at  any 
point  may  be  determined  by  the  graphical  method  of  Fig.  38. 
Having  taken  a  sufficient  number  of  these  points,  and  plotted 
the  corresponding  heat  drops,  we  get  the  broken  curve  marked 
"stage  drops,"  the  breaks  being  as  shown  in  dotted  lines.  The 
average  ordinate  of  this  curve  gives  the  average  of  the  heat 
drops  for  all  the  stages,  which,  in  this  case,  =3.58  B.  T.  U.  This 
average  drop,  divided  into  the  total  heat  drop  from  inlet  to 
exhaust,  will  give  the  total  number  of  stages.  The  total  heat 


CALCULATIONS  OF  TURBINE  BLADING. 


61 


drop,  determined  from  the  steam-entropy  tables,  or  from  the 
heat-entropy  chart  (see  Fig.  40)  is  found  to  be  338  B.  T.  U.,  for 
pure  adiabatic  expansion,  but  there  is  a  loss  of  energy  in  the 
steam  of  y  =  28  % ;  therefore  338  X  ( 1  -  28)  =  338  X  .  72  =  243 
B.  T.  U.  Actual  heat  drop  per  pound  of  steam. 


Curve  of  Net  Voll  per  Ib.  of  Steam, 
FIG.  39. — Pressure  and  volume  curves,  single-flow,  impulse-reaction  turbine. 


The  number  of  stages  then  will  be  the 
Total  heat  drop          243  B.  T.  U. 


=68  instead  of  66. 


Average  stage  drop     3 . 58  B.  T.  U. 

The  68  stages  may  be  laid  off  on  the  base  AB  and  the  cylinders, 
which  have  up  to  this  point  been  divided  only  tentatively,  may 
be  readjusted,  as  shown  in  full  lines.  The  division  made  here  is 
as  follows: 


Heat  Drop,  as  Scaled 
from  Curve 

First  cylinder 

32  stages 

43 

Second  cylinder 

.  18  stages 

54 

Third  cylinder  
Fourth  cylinder  

11  stages 
7  stages 

64 

82 

Total 

68  stages 

243 

62  STEAM  TURBINES. 

The  progressive  heat  drop  through  the  turbine  may  be  shown 
in  a  curve  (see  Fig.  39)  in  which  the  ordinates  represent  the 
progressive  sum  of  the  heat  drops  from  A.  The  last  ordinate 
should  check  with  the  total  net  heat  drop  243  B.  T.  U. 

By  the  initial  conditions  there  are  further  losses  amounting 
to  24%  of  the  actual  heat  drop.  Therefore,  243x76%  =  185 
B.  T.  U.  per  pound  of  steam,  are  available  for  power.  Then 

1980000 

-  =13.8  pounds  of  steam  per  B.  H.  P. 


185X777.5 
Since  the  efficiency  of  the  generator  =  94%, 

13.8X1.36 

=  20  pounds  =  steam  per  K.  W.  hour. 

.  i/4 

2000  X  20 

=11.1   pounds   steam    per  second  for   normal   load. 

3600 

The  steam  rate  may  rise  slightly  for  overloads,  but  hardly 
enough  to  change  the  rate  inside  of  20%  overload;  we  have 

20  X  2400 

therefore  =13.4  pounds  steam  per  second  for  overload 

3600 

conditions.  Where  a  by-pass  valve  is  used,  as  in  Fig.  55,  the 
steam  rate  should  be  further  raised  for  the  blading  beyond  it. 

There  remains  the  determination  of  the  steam  volume  under 
the  given  conditions,  and  of  the  dimensions  of  the  blades  and 
vanes.  The  condition  of  the  steam  may  be  taken  from 
Fig.  40,  which  is  taken  from  the  heat  chart.  A,  as  before, 
indicates  the  initial  conditions.  The  vertical  drop  to  B  on  the 
1  pound  line  gives  a  quality  of  79.2%.  But  the  28%  energy 
loss  raises  the  quality  of  the  exhaust  to  88.5%.  The  condition 
curve  gives  the  quality  of  the  steam  for  any  intermediate 
pressure. 

The  heat  drop  for  any  point,  read  off  from  the  curve  of  total 
drops,  Fig.  39,  and  applied  to  Fig.  40  by  measuring  down  from 
A  and  projecting  over  to  the  quality  curve  AD,  gives  the  pres- 
sure and  condition  corresponding  to  the  pressure.  Curves  of 
pressure  and  volume  of  Fig.  39  may  thus  be  derived. 

The  blade  lengths  may  be  derived  as  follows:  From  Eq.  (14) 
the  area  of  the  steam  passage  required,  in  square  inches,  = 

weight^fjteam  per  second  X  vol.  per  pound  X  144 
steam  velocity  in  feet  per  second. 


CALCULATIONS  OF  TURBINE  BLADING.  63 


and  the  length  of  blade  required  to  give  the  necessary  area 
(assuming  the  blades  as  occupying  1/3  of  the  clear  passageway, 
and  the  blade  angle  =  24°)  is 

Area  X  1.5  1.5  A 


~ 


7rXmean  blade  dia.  sin  24 


FIG.  40.  —  Condition  curve,  single-flow  impulse-reaction  turbine. 

Combining  these  equations  and  reducing, 


.  5  _      1  7  1  .  5  v 
AxVd  ~~  Vd    ' 


For  the  normal  load,  2000  K.W.,TF=11.  1  pounds  (p.  62). 
For  the  overload,         2400  K.  W.,W  =  13.4  pounds  (p.  62)  . 


64  STEAM  TURBINES. 

The  mean  blade  diameter,  d,  for  the  various  cylinders,  is 
determined  from  the  values  of  u,  Fig.  38,  and  the  initial  con- 
dition of  3,600  R.  P.  M.,  or  60  revolutions  per  second. 

u  =  6QXxXd,  from  which 

120 

For  first  cylinder        d  =  — -  =  .635'=   7  5/8  ins.  mean  dia. 
.toy 

For  second  cylinder  d  =  -—=  .875' =  10  1/2  ins.  mean  dia, 

loc/ 

095 

For  third  cylinder      d  = =  1. 19' =  14  1/4  ins.  mean  dia. 

ic?y 

320 
For  fourth  cylinder   d  = =  1.7'   =20  1/2  ins.  mean  dia. 

lOc/ 

For  a  slower  R.  P.  M.  or  higher  blade  velocities  the  mean  blade 
diameters  would  of  course  be  correspondingly  larger. 

Taking  V  from  the  curve  V,  Fig.  38,  and  volumes  from 
Fig.  39,  and  with  the  values  for  w  and  d  above,  the  lengths  of 
the  various  blades  may  be  determined.  For  manufacturing 
reasons  the  lengths,  instead  of  increasing  progressively  along  the 
rotor,  are  stepped  into  groups  as  shown  in  Fig.  44. 

Problems. 

1.  Make  diagrams  and  calculations  for  the  blading  of  a  single  flow 
Parsons  turbine,  having  four  drums. 

Capacity,  rated,  1000  K.  W. 

Capacity  at  opening  of  by-pass  valve,   1300  K.  W. 
Initial  pressure,  150  gauge. 

Superheat,  50°  F. 

Exhaust  pressure,  28  1/2  in.  vac. 

R.  P.  M.,  3600. 

Exit  blade  angles,  25°. 

Steam  velocities,  250  ft.  to  1000  ft. 

Blade  velocities,  150  ft.  to  350  ft. 

Losses  and  generator  efficiency,  as  given  on  p.  62. 

2.  Make  diagrams  and  calculations  for  the  blading  of  a  single  flow 
L.  P.  turbine  of  Parsons  type. 

Initial  steam  pressure,  16  Ibs.  absolute. 

Quality,  95%. 

Exhaust,  28  1/2  vacuum. 

R.  P.  M.,  3600. 
Exit  blade  angles,  28°. 


CALCULATIONS  OF  TURBINE  BLADING. 


66  STEAM  TURBINES. 

Assume  same  steam  and  blade  velocities  as  for  the  low  pressure 
stages  of  Prob.  1. 

3.  Report  on  the  Avery  turbine,  interesting  as  being  a  pure  reaction 
turbine  and  probably  the  first  commercial  one.     See  American 
Machinist,  Nov.  9,  1905,  p.  631. 

4.  Report  on  the  article  on  Blading  Calculation,  Power,  Aug.  9, 1910, 
p.  1412. 

5.  Report  on  article  on  Construction  Details  of  a  Reaction  Turbine, 
Power,  May  19,  1908,  p.  761. 

6.  Report  on  article  on  the  Internal  Losses  in  a  Parsons  Turbine,  by 
Prof.  A.  G.  Christie.    Power,  Aug.  24,  1909,  p.  299. 

References. 

STODOLA:     "The  Steam  Turbine." 

THOMAS:     "Steam  Turbines." 

MOYER:     "Steam  Turbines." 

HODGKINSON:    Paper,  A.  S.  M.  E.,  vol.  xxv. 

PARSONS:     Paper,  Inst.  Naval  Arch.  (London),  May,  1904. 

See  also  references  in  the  following  problems. 

Art.   14. — Double  Flow  Impulse -reaction  Turbines. 

On  account  of  the  drop  in  pressure  through  the  moving  blades 
in  the  Parsons  turbine  steam  must  be  admitted  around  the  entire 
circumference,  which  leads  to  very  short  blades  in  the  high- 
pressure  stages,  and  for  the  same  reason  the  clearance  over  the 
ends  of  the  blades  must  be  very  small.  Leakage  is  further 
minimized  by  using  only  small  pressure  drops,  which  increases 
the  number  of  H.  P.  stages,  lengthens  the  rotor,  and  introduces 
trouble  from  expansion  which  in  the  larger  sizes  becomes  serious. 
While  the  heat  drop  per  stage  is  less  at  the  H.  P.  end  of  the  rotor 
than  at  the  L.  P.  end,  the  pressure  drop  is  greater.  This,  coupled 
with  the  fact  that  the  end  clearances  over  the  short  H.  P.  blades 
must  inevitably  give  a  greater  percentage  of  leakage,  makes  the 
H.  P.  end  of  a  Parsons  turbine  its  least  efficient  portion.  The 
pure  reaction  type,  where  the  blades  are  pressure  balanced  and 
admission  may  be  had  through  a  portion  only  of  the  blade  circle, 
is  more  efficient  in  the  high-pressure  ranges  than  the  reaction 
type,  but  in  the  later  stages  where  water  is  present  in  the  steam 
it  is  less  efficient. 

These  considerations  have  led  to  the  combination  of  the  two 
types  in  one  machine,  utilizing  the  advantages  of  both,  Steam 


CALCULATIONS  OF  TURBINE  BLADING. 


67 


68 


STEAM  TURBINES. 


is  admitted  through  nozzles  to  a  multi-stage  impulse  wheel  and 
expanded  to  about  atmospheric  pressure.  The  rest  of  the  ex- 
pansion takes  place  in  fixed  and  moving  blades  of  impulse- 
reaction  type.  The  reaction  portion  is  divided  in  the  latest 
form  and  steam  flows  axially  in  both  directions  from  the  impulse 
wheel.  Fig.  42  shows  a  Westinghouse  turbine  of  this  design 
where  the  central  impulse  wheel  is  clearly  seen,  with  the  reaction 
portions  on  each  side.  Fig.  43  is  a  sectional  elevation  of  the 
same  turbine  and  shows  clearly  the  course  of  the  steam  as  it 
leaves  the  impulse  wheel  and  is  divided  into  two  streams  flowing 
in  opposite  directions.  This  arrangement  automatically  balances 


[—Exhaust  h-  Exhaust 

FIG.  43.— Section  of  10,000-K.  W.  Westinghouse  double-flow  turbine. 

the  end  thrust  of  the  reaction  blades  and  eliminates  the  balancing 
pistons  necessary  in  the  single-flow  type.  Besides  a  symmetrical 
casing,  with  smaller  exhaust  connections  it  materially  shortens 
the  distance  between  the  bearings.  Fig.  44  shows  two  rotors, 
both  for  2000-K.W.  Westinghouse  machines,  the  upper  one  of 
the  double-flow  combined  type  and  the  lower  the  old  single-flow 
type. 

Double-flow  turbines  are  found  most  desirable  in  the  larger 
sizes,  but  for  comparison  with  the  previous  problem  of  a  single-flow 
turbine,  let  the  same  conditions  be  assumed  for  one  of  this  type. 
Let  the  steam  be  expanded  in  a  set  of  nozzles  from  inlet  pressure 
to  25  pounds  absolute  and  pass  through  two  velocity  stages  of 
an  impulse  wheel  of  the  Curtis  type  as  shown  in  stage  a,  Fig.  29. 
Let  the  remainder  of  the  expansion  to  1  pound  absolute  take 
place  in  two  sets  of  Parsons  blading  as  in  Fig.  42.  Let  the 


CALCULATIONS  OF  TURBINE  BLADING.  69 

osses  in  the  impulse  element,  due  to  disc  and  blade  friction, 
leakage,  etc.,  be  assumed  as  40%,  the  energy  so  lost  reappearing 
in  the  increased  quality  of  the  steam.  The  friction  losses  in  the 
low-pressure  blading  will  be  taken  at  28%  as  before. 

Fig.  45  gives  the  expansion  diagram  for  these  conditions. 
The  net  drop  available  for  the  impulse  stage  is  91.2  B.  T.  U. 
and  for  the  low-pressure  stages  142.8  B.  T.  U.  It  will  be  seen 
from  last  article  that  the  number  of  stages  in  the  low-pressure 


FIG.  44. — Comparison  of  single-  and  double-flow  Westinghouse  rotors — 3600  and   1800 
R.  P.  M.^ame  H.  P. 

blading  depends  on  the  available  heat  drop,  the  steam  and  blade 
velocities  and  the  exit  angles.  Dividing  the  flow  does  not  affect 
the  number  of  stages  on  each  side.  It  merely  halves  the  length 
of  the  blades,  an  advantage  in  the  last  few  stages  where  in  the 
single-flow  machines  the  length  is  excessive.  Greater  blade 
angles  may  be  used  to  advantage  in  low-pressure  stages  than  in 
high-pressure  ones  without  unduly  increasing  the  number  of 
stages,  and  30°  will  be  used  instead  of  24°  as  before. 

Let  the  blading  be  carried  on  two  drums  or  cylinders  running 
at  225  and  320  feet  per  second  and  the  steam  velocity  increase 
from  400  feet  per  second  to  950.  This  gives  the  same  conditions 
as  for  the  last  two  drums  in  Fig.  38. 

If  3/8  of  the  total  work  be  carried  by  the  impulse  wheel,  1/4 


70 


STEAM  TURBINES. 


by  the  smaller  drums,  and  3/8  by  the  larger  ones,  the  application 
of  formula  (27)  gives  13  stages  and  9  stages  for  the  ^  first  and 
second  drums,  respectively.  Laying  these  off  tentatively  and 
proceeding  as  in  Fig.  35  we  find  the  mean  stage  drop  to  be 
6.8B.  T.  U.  (Fig.  46).  Then 

—  =  21  =  number  of  stages. 

6.8 


FIG.  45. — Condition  curve,  double-flow  turbine. 

Re-adjusting  we  may  take  13  for  the  first  cylinders  and  8  for 
the  second.  The  stage  drops  are  laid  off  in  Fig.  45,  those  from 
B  to  C  being  on  the  first  cylinder,  and  those  from  C  to  D  on  the 
second.  The  pressures  and  conditions  are  found  directly  and 
the  blade  lengths  determined  as  in  the  last  article,  which  will 
be  those  for  a  single-flow  turbine  of  21  rows.  In  the  present 


CALCULATIONS  OF  TURBINE  BLADING. 


71 


one  there  will  be  two  complete  sets  of  blades  of  21  stages  each, 
each  set  of  blading  one-half  the  length  required  for  the  single- 
flow.  Curves  of  pressures  and  net  volumes  per  pound  of  steam 
are  shown  in  Fig.  46. 

It  must  be  remembered  that  in  this  and  the  foregoing  articles 
certain  constants,  velocities  and  friction  coefficients  have  been 


Vssumed  Curve_ofSteamVeloci 
Curve  of  StagePv 


B  C 

FIG.  46. — Velocity  curves  and  heat  drops,  double-flow  turbine. 

more  or  less  arbitrarily  assumed.  Accurate  values  for  these 
can  be  assumed  only  after  wide  experience  and  from  intimate 
knowledge  of  working  conditions.  Such  information  on  the 
choice  of  values  as  is  available  may  be  found  in  the  standard 
works  on  turbines  referred  to  at  the  end  of  this  article. 

Problems. 

\  / 1.  Calculate    the    blading    and    draw   diagrams   for    a   double-flow 
turbine  similar  to  Fig.  43. 

Capacity,  2000  K.  W. 

Initial  steam  pressure,  160  Ibs.  gauge. 

Superheat,  60°. 

Exhaust  pressure,  28  ins.  vac. 

Impulse  wheel  to  have  two  velocity  stages  and  to  carry  expansion 
down  to  20  Ibs.  absolute,  with  reheating  losses  of  40%. 


72  STEAM  TURBINES. 

2.  Make  diagrams  and  blade  calculations  for  a  turbine  for  conditions 
similar  to  Prob.  1.     The  first   pressure  stage  to   be  a  two-stage 
Curtis  wheel  expanding  to  25  Ibs.  absolute.     The  remainder  of  the 
expansion  to  take  place  in  a  series  of  wheels  of  Rateau  or  multi- 
cellular  type  (Fig.  30) .     Consult  J.  A.  Moyer,  Steam  Turbines,  p.  86. 

3.  Report  on  the  Westinghouse  double  flow  turbine  described  in 
Power,  June  16,  1908,  p.  931. 

4.  Report  on  the  construction  and  test  of  a  10,000-K.  W.  double-flow, 
impulse-reaction  turbine,  described  in  paper  by  Naphtaly,  Trans. 
A.  S.  M.  E.,  vol.  xxxii,  Dec.,  1910.     (Shown  in  Fig.  43.) 

5.  Report  on  the  Melms-Pfenninger  turbine  (Curtis-Parsons),  described 
in  Lond.  Engineering,  July  9,  1909,  p.  39,  and  Power,  Sept.,  1907, 
p.  643. 

References. 

MOYER:     " Steam  Turbines." 
STODOLA:     "The  Steam  Turbine." 

NAPHTALY:     "Test  of  10000-K.  W.  Turbine,"  Trans.  A.  S.  M.  E.,  Dec., 
1910. 


CHAPTER  IV. 
MECHANICAL  PROBLEMS. 

The  problems  already  considered  have  dealt  with  the  using 
of  steam  at  the  high  velocities  of  turbine  practice.  These 
involve  problems  of  a  purely  mechanical  nature,  among  which 
are  provision  for  centrifugal  strains  due  to  speeds  of  3,000  to 
30,000  R.  P.  M.,  the  balancing  of  the  shafts,  bearings  suitable 
for  such  speeds,  and  close  and  rapid  regulation  under  varying 
loads. 

Art.   15. — Centrifugal  Strains. 

A  thorough  consideration  of  this  subject  involves  extended 
and  complex  analysis.  Some  only  of  its  phases  will  be  touched 
on  here. 

As  the  velocities  in  the  De  Laval  turbine  are  much  higher 
than  in  any  other,  it  is  in  this  turbine  that  the  interesting  be- 
havior of  a  disc  rotating  at  high  velocities  is  most  marked. 

If  a  flexible  shaft  carry  a  round  disc,  one  side  of  which  is 
slightly  heavier  than  the  other,  the  center  of  gravity  will  lie  at 
one  side  of  the  geometrical  center,  as  in  Fig.  47  "a".  If  they 
are  rotated  rapidly  the  unbalanced  centrifugal  force  of  the  heavy 
side  will  deflect  the  shaft  toward  the  heavy  side,  and  cause  the 
geometrical  center  of  the  disc  to  describe  a  circle  as  at  "b".  This 
action  increases  with  the  speed  up  to  a  certain  point  called  the 
"critical  speed,"  when  the  vibration  becomes  momentarily 
excessive.  On  further  increase  of  speed  they  settle  down  and 
will  run  quietly,  however  much  the  speed  be  increased.  At 
this  critical  speed  the  axis  of  rotation  shifts  from  the  center  of 
the  path  of  the  geometric  center,  o,  to  the  center  of  gravity  of 
the  wheel,  as  shown  in  Fig.  47  "c". 

It  can  be  shown  that  the  deflection  is 
e 

v=  —^ 

'-•fe 

73 


74 


STEAM  TURBINES. 


where  e  is  the  eccentricity  of  the  center  of  gravity  and  Vc  the 
critical  velocity  referred  to.  The  greater  the  velocity  V, 
the  smaller  y  becomes,  approaching  the  value  y  =  e,  until  the 
wheel  bursts.  In  the  De  Laval  practice  the  critical  speed  is 
from  1/8  to  1/5  of  the  normal  R.  P.  M. 


FIG.  47.— Action  of  the  flexible  shaft. 


For  cylindrical  rings  where  the  radial  thickness  is  small,  the 
tensional  stress  due  to  the  centrifugal  force  is  equal  to 


12  w 


(29) 


where  S  =  stress  in  pounds  per  square  inch. 
w  =  weight  per  cubic  inch  of  material. 
v  =  linear  velocity  of  ring  in  feet  per  second 


MECHANICAL  PROBLEMS. 


75 


Calculation  of  the  stresses  in  discs  rotating  at  very  high  speeds 
is  difficult.  They  vary  with  the  weight  of  the  material  and  the 
square  of  the  speed.  Fortunately  the  materials  available  have 
been  so  improved  that  a  factor  of  safety  can  be  used,  sufficient 


FIG.  48. — Large  and  small  De  Laval  wheels. 

to  cover  any  uncertainty  as  to  the  centrifugal  strains.  Two 
facts  are  shown  clearly  by  both  theory  and  experiment. 

First.  The  stresses  are  greater  nearer  the  center  than  near 
the  rim. 

Second.  The  stress  in  the  nave  of  a  bored  disc  is  greater  than 
in  a  solid  disc.  A  small  hole  may  even  double  the  strains. 


76  STEAM  TURBINES. 

These  principles  have  been  recognized  in  the  design  of  the 
disc  in  the  De  Laval  turbine  shown  in  Fig.  48.  The  profile  is 
a  form  of  logarithmic  curve  asymptotic  to  the  central  axis  of 
the  disc.  In  the  smaller  turbines  the  flexible  shaft  runs  through 
the  disc,  but  in  the  larger  ones  the  shafts  are  flanged  to  the  sides, 
to  avoid  piercing  the  disc.  The  curved  lines  added  near  the 
center  of  the  large  wheel  show  the  theoretical  form,  to  which 
the  attachments  are  tangent.  Wheels  of  this  form,  when 
tested  to  destruction,  would  burst  through  the  center  into 
large  pieces,  and  it  is  stated  that  these  pieces  have  been 
driven  through  a  steel  wheel  case  2  inches  thick.  This  menace 
is  obviated,  however,  by  turning  grooves,  A,  A,  which  reduce 
the  thickness  of  the  wheel  close  to  the  periphery,  decreasing 
the  strength  of  the  wheel  at  this  point  so  that  the  stresses 
here  are  about  50%  higher  than  in  the  rest  of  the  wheel.  The 
factor  of  safety  at  this  point  being  about  5,  the  rim  of  the  wheel 
will  tear  off  at  a  little  over  twice  the  normal  speed,  breaking  up 
into  small  fragments,  which  are  unable  to  damage  the  wheel 
case.  When  the  rim  lets  go,  the  blades  which  are  the  impelling 
force  of  the  wheel  go  with  it,  the  centrifugal  forces  are  at  once 
much  reduced,  and  the  wheel  is  unbalanced.  The  heavy  hub 
which  projects  into  the  casing  at  B  with  but  small  clearance 
comes  into  contact  with  the  sides  and  acts  as  a  brake,  bringing 
the  wheel  to  rest  in  a  few  revolutions.  Discs  of  rolled  plate  are 
not  used  for  a  single-stage  machine,  as  streaks  or  lines  of  weak- 
ness, due  to  "piping,"  difficult  to  detect,  may  become  elements 
of  danger. 

In  connection  with  the  improvement  in  materials  referred  to, 
it  may  be  noted  that  Krupp  and  Co.  of  Essen,  Germany,  have 
for  this  use  a  special  nickel  steel  of  125,800  pounds  tensile 
strength,  92,300  pounds  elastic  limit,  and  12%  elongation. 
They  have  recently  produced  nickel  steel  of  even  higher  strength 
but  of  less  elongation.  The  following  figures  are  taken  from 
their  published  tables: 


MECHANICAL  PROBLEMS. 


77 


Ult.  Tensile  Strength, 
Pounds  per  Sq.  Inch 

Elastic  Limit, 
Pounds  per  Sq.   Inch 

255,600 

7. 

136,320 

Measured 

252,760 

5.5 

153,360 

on  .472  inch 

251,340 

6. 

210,160 

diam.  bar, 

258,440 

4.1 

227,200 

3  .  937  between 

211,580 

6.8 

187,440 

points. 

310,980 

(?)' 

213,000 

Broke  in  center  punch  mark. 


FIG.  49. — Section  of  rotor,  five-stage  Curtis  turbine. 

These  elastic  limits  are  erratic,  but  the  results  are  remarkable. 
It  is  a  question  whether  such  hard  material  is  practical  but  discs 


78  STEAM  TURBINES. 

are  used  which  show  under  test  134,900  pounds  tensile  strength, 
14%  elongation,  and  106,630  pounds  elastic  limit.. 

In  multi-stage  impulse  turbines  where  the  velocity  is  about 
half  that  of  the  single-stage  type,  the  question  of  centrifugal 
strains  is  not  so  difficult.  In  the  Curtis  turbine  the  wheels  are 
built  up  of  castings  and  plates.  The  blades  are  milled  in  a 
sectional  blade  ring  bolted  to  the  discs  at  the  edge.  Fig.  49 
shows  the  detail  of  this  construction. 

In  turbines  of  the  Parsons  type  the  velocities  are  still  further 
reduced  (see  table,  p.  56).  The  principle  adopted  by  Mr.  Parsons 
was  to  have  the  drum  and  shaft  stiff,  balanced  as  closely  as  pos- 
sible, and  carried  in  a  bearing  which  would  provide  sufficient 
lateral  motion  to  allow  the  shaft  to  find  its  own  center. 

Problems. 

i.  Report  on  the  conclusions  of  paper  on  "Critical  Speed  Calculations." 
by  S.  H.  Weaver,  Jour.  A.  S.  M.  E.,  vol.  xxxii,  June,  1910. 

References. 

STODOLA:     " The  Steam  Turbine"     (especially  4th  ed.). 
JUDE:     "Theory  of  the  Steam  Turbine." 
MOYER:     "Steam  Turbines." 
J.  M.  NEWTON:     "Design  and  Construction  of   High  Speed  Turbine 

Rotors,"  London  Engineering,  July  8  and  15,  1910. 
WEAVER:     "Critical   Speed   Calculation,"    Jour.  A.   S.   M.   E.,  June, 

1910. 

Art.  1 6. — Bearings. 

The  earlier  form  of  bearing  used  by  Parsons  is  shown  in  Fig. 
50,  where  the  space  between  the  shaft  and  the  journal  wall  was 
taken  up  by  two  sets  of  rings.  Those  of  one  set  fitted  the  shaft 
closely,  and  had  play  between  their  outer '  diameters  and  the 
journal  wall.  Those  of  the  other  set,  which  alternated  with 
these,  fitted  the  journal  box  tightly,  and  were  loose  on  the  shaft. 
They  were  held  in  contact  by  a  side  spring.  A  lateral  movement 
of  .005  inch  or  more  was  thus  provided.  This  arrangement,  while 
satisfactory,  has  been  superseded  by  one  (Fig.  51)  in  which  there 
is  a  nest  of  bronze  sleeves  concentric  with  the  shaft,  each  having 
about  .  002  inch  play  on  the  diameter.  Holes  are  bored  through 
them  to  permit  the  lubricating  oil  to  reach  the  inner  sleeves  and 
shaft.  Side  play  is  thus  provided  as  before,  but  with  a  much 


MECHANICAL  PROBLEMS. 


79 


simpler  construction.  In  the  large  machines,  running  below 
1200  R.  P.  M.,  the  flexible  bearing  is  dispensed  with  and  solid 
self -oiling  bearings  are  used. 

In  the  vertical  Curtis  turbine  the  problem  has  been  to  design 


FIG.  50. — Old  Parsons  shaft  packing. 

a  step  bearing  which  would  carry  the  entire  weight  of  the  shaft, 
wheels,  and  the  field.  The  end  of  the  shaft  carries  a  cast  iron 
block,  which  runs  upon  a  similar  block  in  the  bearing.  Oil  or 
water  is  forced  through  the  pipe  ^l,Fig.  52,  into  the  recessed 
portion  between  the  bearing  faces,  and  circulates  out  and 


FIG.  51. — Later  Parsons  shaft  packing. 

upward,  through  the  journal,  leaving  the  bearing  at  the  top  13. 
The  entire  weight  of  the  moving  parts  is  thus  carried  on  the 
film  of  lubricant  between  the  blocks  a  and  6.  The  pressure  of 
the  lubricant  is  from  150  pounds  to  900  pounds  per  square  inch, 
according  to  the  size. 


80 


STEAM  TURBINES. 
Problems. 


1.  Report  on  the  principles  of  labyrinth  packings,  see  Power,  Sept. 
1908,  p.  401. 

2.  Report  on  the  general  principles  of  the  labyrinth  packing,  i 
Lond.  Engineering,  Jan.  10,  1908,  p.  35. 


FIG.  52. — Step  bearing  of  a  Curtis  vertical  turbine. 


References. 

STODOLA:     "The  Steam  Turbine"  (4th  ed.). 

JUDE  :     "  Theory  of  the  Steam  Turbine." 

For  theory  of  the  labyrinth  packing  see  London  Engineering,  Jan.  10, 

1908,  p.  35,  also  "Power,"  Sept.  8,  1908,  p.  401. 
Revue  de  Mechanique,  Nov.,  1910. 


MECHANICAL  PROBLEMS. 


82  STEAM  TURBINES. 

Art.  17. — Governing. 

There  are  three  types  of  turbine  governors  in  general  use: 

First,  balanced  throttling  valves. 

Second,  multiple  closing  or  relay  valves. 

Third,  intermittent  admission. 

The  well  known  turbines  present  examples  of  all  three  of  these 
classes.  A  fourth  method  of  control  is  used  in  conjunction  with 
the  third  as  supplementary  to  it.  It  consists  of  means  for 
admitting  H.  P.  steam  directly  to  the  later  stages  by  means  of  a 
by-pass  valve,  in  order  to  provide  for  heavy  overload  conditions. 

Throttling  Type. 

As  applied  on  the  DeLaval  turbine,  this  governor  has  a  spring- 
actuated  double-beat  valve,  controlled  by  a  spring  and  weight 
governor  located  at  one  end  of  one  of  the  gear  shafts  where  the 
speed  has  been  reduced  10  to  1.  Even  here  the  speed  is  from 
1,000  to  3,000  R.  P.  M.  This  high  velocity  alters  the  weight 
arms  materially  from  the  well  known  shape,  and  they  take 
the  form  of  semi-cylindrical  leaves,  D,  turning  about  the  knife 
edges,  and  closely  enfold  the  controlling  spring.  The  governing 
mechanism  has  a  further  control  in  addition  to  that  of  the 
throttle.  If  the  balanced  valve  fails  to  govern  and  the  speed 
continues  to  rise,  the  tappit,  P,  comes  into  contact  with  an 
independent  valve,  operating  a  butterfly  valve,  V,  in  the  ex- 
haust passage  and  raising  the  back  pressure.  This  immediately 
puts  a  brake  on  the  wheel  and  prevents  any  further  accelera- 
tion of  speed.  The  effectiveness  of  this  action  may  be  shown  by 
the  fact  that  a  150  H.  P.  turbine,  with  nozzles  designed  for  150 
pounds  gauge  pressure,  and  26  inches  vacuum,  if  operated  on  a 
back  pressure  equivalent  to  an  atmospheric  exhaust,  will  slow 
down  and  can  not  be  brought  up  to  full  speed  even  with  the 
entire  load  removed. 

The  controlling  mechanisms  of  the  De  Laval,  Kerr,  Zoelly,  and 
a  large  number  of  other  turbines  follow  these  general  lines. 

Multiple  or  Relay  Control. 

In  the  smaller  sizes  of  Curtis  turbines  governing  is  effected  by 
throttling,  as  already  described.  In  the  larger  sizes  the  speed  is 
controlled  by  the  opening  and  closing  of  small  valves  admit- 


MECHANICAL  PROBLEMS. 


83 


1.  Govenor. 

2.  Steam   Chest. 


Nozzle 

Moving  Blades 
Stationary  Blades 
Moving  Blades 


—Stationary  Blades 
Movmg  Blades 


1        I      J, 

Fro.  54. — Relay  control  of  Curtis  turbine. 


STEAM  TURBINES. 


MECHANICAL  PROBLEMS. 


85 


ting  to  the  separate  nozzle  sections,  as  shown  in  the  lower  part  of 
Fig.  54,  which  is  a  schematic  section  of  the  casing  2  above,  the 
number  in  action  depending  upon  the  load.  These  nozzle 
valves  are  operated  from  the  governor  mechanism,  1,  at  the  top 
of  the  unit,  and  are  designed  to  be  fully  open  or  shut,  like  a 
pop-safety  valve,  in  order  to  prevent  cutting  of  the  seats  by 
wire  drawing.  The  control  of  the  nozzle  valves  by  the  governor 
has  been  effected  by  means  of  positive  mechanical  connections, 
electrical  connections,  and  hydraulic  cylinders.  The  last  has 
been  found  most  satisfactory,  and  is  used  on  the  later  machines. 
This  method  of  control  by  multiple  valves  gives  excellent 
economy,  as  the  steam  is  used  at  an  almost  constant  thermo- 
dynamic  efficiency,  whatever  the  load. 

Intermittent  Control. 

The   general   arrangement   of  the   controlling   mechanism  is 
shown  on  the  general  section  of  a  Westinghouse  turbine,  Fig.  55. 


FIG.  56. — Governing  mechanism  of  the  Westinghouse  turbine. 

Admission  is  through  a  single  double-beat  valve  controlled  by 
a  steam-operated  piston  above  it,  Fig.  56.  A  heavy  spring 
above  the  piston  tends  to  hold  the  valve  to  its  seat.  Steam  is 


86 


STEAM  TURBINES. 


admitted  to  the  piston  B  through  the  annular  clearance  X,  around 
the  valve  steam  and  exhausts  through  a  controlling  valve 
A,  which  is  actuated  by  the  governor.  The  governor  is  of  the 
bell-crank  type,  the  horizontal  arms  bearing  against  an  ad- 
justable spiral  spring.  E  and  D  are  fixed  fulcrums,  F,  a 
floating  one,  moving  up  and  down  with  the  governor  sleeve. 
C  is  an  oscillating  lever  driven  by  worm  gearing  and  an  eccentric, 
from  the  main  turbine  shaft.  The  motion  of  C  is  communicated 
to  the  pilot  valve,  A,  and  thence  to  the  main  valve,  admitting 
steam  to  the  turbine  in  gusts.  The  distance  that  the  valve  A 
opens  as  it  moves  up  and  down,  and  consequently  the  time  it 


&  1BO 

SI    125 


fi      75 
5      '0 


26 

Atmos- 
pheric^ 

Absolute 
Zero 


8 
2210     O 


FIG.  57. — Pulsation  diagram,  Westinghouse  turbine. 

remains  open,  is  controlled  through  F  by  the  position  of  the 
governor.  At  light  loads  the  main  valve  opens  for  only  short 
periods  and  remains  closed  for  the  greater  part  of  the  stroke  of  A. 
As  the  load  increases  the  valve  remains  open  longer,  until  finally 
a  practically  continuous  pressure  is  maintained  in  the  H.  P.  end 
of  the  turbine.  The  effect  of  the  governor  on  the  initial  pressures 
is  shown  in  Fig.  57.  The  fourth  method  of  control,  that  of 
providing  for  overloads  by  admission  of  steam  to  later  stages  is 
also  shown  in  Fig.  55  where  a  secondary  admission  valve  Vs  is 
provided,  to  admit  high  pressure  steam  to  the  second  drum  of 
the  turbine  for  overloads.  It  is  not  opened  and  closed  regularly, 
as  the  main  one  is,  but  is  controlled  by  another  pilot  valve  con- 
nected directly  with  the  governor  sleeve.  Another  device  for 
accomplishing  the  same  thing,  used  by  Brown,  Bovari,  and  Co. 
in  Europe,  opens  by-pass  valves  to  the  later  stages  as  the  pres- 


MECHANICAL  PROBLEMS.  87 

sure  rises  in  the  H.  P.  chamber.  It  is  obvious  that  steam 
admitted  directly  to  the  later  stages  is  not  used  to  the  greatest 
advantage,  but  as  overload  conditions  are  intermittent  the  loss 
in  steam  economy  is  admissible. 

A  comparison  of  tests  of  turbines  using  the  three  methods  of 
governing1  shows  that  from  the  standpoint  of  steam  consump- 
tion under  light  loads  the  multiple  valve  control  is  most  economi- 
cal, intermittent  admission  next  and  throttling  valve  last.  The 
throttling  governor  is,  however,  the  simplest  and  is  used  almost 
universally  on  small  units. 

Problems. 

1.  Look  up  and  report  on  the  various  methods  of  operating  the  multiple 
nozzle  valve  on  the  Curtis  turbine,  see  Bulletins  of  the  General 
Electric  Co. 

2.  Report  on  the  regulation  of  the  Rateau  low  pressure  turbine,  de- 
scribed in  Power,  May  10,  1910,  p.  845. 

References. 

STODOLA:     "The  Steam  Turbine"  (4th  ed.). 
JUDE  :     "  Theory  of  the  Steam  Turbine." 
MOVER:     " Steam  Turbines." 
Revue  de  Mechanique,  Oct.,  1910. 

1  Mechanical  Engineer,  Jan.  20,  1906. 


CHAPTER  V. 
COMPARISON  OF  TYPES. 

Art.  1 8.— Vertical  Turbines. 

Up  to  the  introduction  of  the  Curtis  turbines  no  one  seems  to 
have  thought  of  arranging  the  shaft  to  run  vertically,  influenced, 
perhaps,  by  the  accustomed  position  of  the  reciprocating  engines. 
The  builders  of  this  turbine  adopted  this  position  and  still 
adhere  to  it  for  their  large  units.  Its  use  is  limited  to  self  con- 
tained generating  sets.  The  following  reasons  are  advanced  in 
its  favor. 

1.  Accurate  control  of  the  relative  position  of  its  parts  by 
means  of  the  adjustable  step  bearing.     (Fig.  52.) 

2.  Symmetry  of  design. 

3.  All  bearings  relieved  from  side  strain  and  lateral  wear. 

4.  Friction  practically  eliminated. 

5.  A  short  shaft,  free  from  deflection. 

6.  Small  floor  space. 

7.  Small  foundations. 

The  arrangement,  shown  in  Fig.  54,  unquestionably  has  advan- 
tages. That  it  reduces  friction  to  a  minimum  is  shown  by  the  fact 
that  unless  a  brake  is  applied  a  5,000-K.  W.  unit  will  run  for  four  or 
five  hours  after  steam  has  been  shut  off.  The  elaborate  step  bear- 
ing necessitated,  with  its  system  of  high  pressure,  forced  lubrica- 
tion is  one  of  the  chief  objections,  and  though  little  trouble  seems 
to  have  developed  from  this  source,  it  is  an  object  of  constant 
watching.  The  generator  is  located  above  the  turbine,  ex- 
posed to  the  heat  arising  from  it,  and  to  steam  leaking  past 
the  glands.  While  the  vertical  position  offers  convenient  access 
for  inspection  and  minor  repairs,  it  is  inconvenient  in  case  of 
overhauling.  In  the  horizontal  type  the  turbine  and  generator 
may  be  overhauled  independently,  and  work  can  be  done  simul- 
taneously on  both  ends.  In  the  vertical,  the  machine  has  to  be 
taken  apart  from  the  top  down,  and  the  discs  stripped  off  one 
by  one. 

88 


COMPARISON  OF  TYPES. 


89 


An  interesting  example  of  the  vertical  type  was  built  in  Berlin 
by  the  Allgemeine  Electricitats  Gesellschaft  or  "A. E.G.,"  com- 
bining the  features  of  the  Curtis  turbine  with  those  of  the  Reidler- 
Stumpf .  A  section  of  this  turbine  is  shown  in  Fig.  58.  The  weight 
of  the  moving  parts  was  carried  by  a  thrust  bearing  (B)  between 
the  generator  and  turbine,  and  a  jet  condenser  was  located  at 


FIG.  58. — Section  of  old  A.  E.  G.  turbine. 


the  lower  end  of  the  shaft.  The  steam  exhausted  into  the 
passage  E,  where  it  was  condensed  by  water  sprayed  in  from  the 
side.  The  condensed  water  drained  into  a  centrifugal  pump  on 
the  end  of  the  main  turbine  shaft.  This  arrangement  is  said  to 
have  given  a  high  vacuum,  and  proven  very  satisfactory.  The 
A. E.G.  have,  however,  discontinued  this  vertical  type  and  now 


90 


STEAM  TURBINES. 


FIG.  59. — 100  H.  P.  Terry  steam  turbine,  opened. 


COMPARISON  OF  TYPES. 


91 


build  for  their  larger  sizes  a  horizontal  machine  illustrated  in  Art. 
20.  This  has  a  Curtis  single-pressure,  multi-velocity  stage  wheel 
and  a  low  pressure  end  with  a  number  of  pressure  stages,  each 
having  a  single  velocity  stage.  A  section  of  this  turbine  is  shown 
in  Fig.  66. 

Problems. 

i.  Report  of  paper,  Emmet,  "Steam  Turbine  in  Modern  Engineering," 
Trans.  A.  S.  M.  E.,  vol.  xxv.,  p.  1041. 

References. 

STODOLA  :     ' '  The  Steam  Turbine. ' ' 
THOMAS:     " Steam  Turbines." 
JUDE  :     "  Theory  of  the  Steam  Turbine." 
FRENCH:     " Steam  Turbines." 

EMMET:     Paper,  "Steam  Turbine  in  Modern  Engineering,"  Trans.  A.  S. 
M.  E.,  vol.  xxv. 

Art.  19.— Tangential  Flow  Turbines. 

The  Reidler  turbine  is  one  of  the  few  turbines  which  use  tan- 
gential jets.  The  buckets  for  tangential  wheels  may  have  two 
forms,  those  which  curve  in  one  plane  only,  as  the  Reidler 


FIG.  60. — Bucket  arrangement,  Terry  turbine. 

and  Terry  turbines,  with  the  jet  divided  or  not,  or  they  may 
be  of  the  Pelton  type,  which  curve  in  all  directions.  Prof. 
Rateau  and  Zoelly  both  experimented  extensively  with  the 
divided  bucket,  but  have  abandoned  it  in  favor  of  multicellular 
machines  with  axial  flow.  In  the  Reidler-Stumpf  machines, 


STEAM  TURBINES. 


however,  it  has  been  developed  with  success,  and  these  have 
used  it  in  units  of  2,000  K.  W.  and  over,  having  four  or  more 
stages. 

The  Terry  turbine,  Fig.  59,  is  manufactured  in  this  country.  In 
this,  undivided  tangential  jets  are  used.  The  steam  is  expanded 
in  one  or  more  nozzles  to  exhaust  pressure  and  enters  at  A, 
Fig.  60,  is  deflected  to  one  side,  and  compounded  on  a  single  wheel 
by  looping  back  into  buckets  B,  in  the  casing,  and  returned  from 
these  into  succeeding  buckets  in  the  single  row  on  the  wheel. 


FIG.  61. — Nozzle  arrangement  of  Reidler-Stumpf  Turbine. 

This  reversal  is  accomplished  four  or  five  times,  a  portion  of  the 
steam  escaping  at  each  loop,  through  the  exhaust  openings,  C. 
Some  of  the  dimensions  of  one  of  these  turbines  are: 


Diameter  of  wheel 
Number  of  buckets 
Width  of  buckets 
Pitch  of  buckets 
R.  P.  M. 
Peripheral  velocity 


=  2  feet. 

=  70. 

=2  1/2  inches. 

=  1  inch. 

=  2600. 

=  270  feet  per  second. 


It  developed  30  H.  P.  with  145  pounds  steam  pressure  on  32 
pounds  steam  per  H.  P.  hour.  Remarkable  economy  is  not 
claimed  for  this  type  but  it  gives  a  compact  and  simple  turbine 


COMPARISON  OF  TYPES. 


93 


with  low  cost  and  running  at  moderate  speeds.  In  the  Reidler 
turbines  the  return  loops  are  made  in  separate  sets  of  buckets, 
as  shown  in  Fig.  61. 


FIG.  62. — Section  of  Kerr  turbine. 


The  Kerr  turbine,  developed  by  Mr.  C.  V.  Kerr,  uses  buckets 
of  the  Pelton  divided-flow  type,  mounted  on  discs.  It  is  of 
the  multicellular  type  shown  in  Fig.  30.  The  buckets  are  drop 
forgings,  finished  on  the  inside.  The  stages  are  repeating 


FIG.  63. — Rotor  of  Kerr  steam  turbine. 


sections  with  the  nozzles  increasing  in  number,  as  rendered 
necessary  by  the  expansion  of  the  steam.  The  design  shows 
careful  consideration  of  the  manufacturing  problems  involved, 
and  adaptability  for  commercial  production.  The  speed  of 


94  STEAM  TURBINES. 

the  Terry  and  Kerr  turbines  is  from  1200  to  3,000  R.  P.  M., 
and  they  are  used  direct  connected  for  blowers,  pumps,  and 
generators,  also  for  belt  driving.  The  governors  are  of  the 
throttling  type,  closely  resembling  the  De  Laval. 

Problems. 

1.  Report  on  the  Terry  turbine,  see  Power,  Nov.  1907,  p.  801,  and 
paper  of  Orrok,  A.  S.  M.  E.,  vol.  xxxi,  p.  263. 

2.  Report  on  the  Kerr  turbine  as  described  in  paper  of  G.  A.  Orrok, 
Trans.  A.  S.  M.  E.,  vol.  xxxi,  p.  263,  also  Am.  Machinist,  Mar.  21, 
1907,  p.  415. 

3.  Report  on  Sturtevant  steam  turbine,  see  paper  of  G.  A.  Orrok, 
A.  S.  M.  E.,  vol.  xxxi,  p.  263. 

4.  Report  on  the  Dake  steam  turbine.     See  Power,  December,  1907, 
p.  886,  and  paper  of  Orrok,  A.  S.  M.  E.,  vol.  xxxi,  p.  263. 

5.  Report  on  the  Bliss  turbine  as  described  in  paper  of  G.  A.  Orrok, 
A.  S.  M.  E.,  vol.  xxxi,  p.  263,  and  Power,  August  10,  1909,  p.  250. 

6.  Report  on  the  Richards  turbine  described  in  the  American  Machin- 
ist, November  16,  1905,  p.  660. 

References. 

STODOLA:     "The  Steam  Turbine." 
JUDE  :     "  Theory  of  the  Steam  Turbine." 
See  also  references  in  the  following  problems. 

Art.  20.— Multicellular  Turbines. 

As  mentioned  before,  Prof.  Rateau's  investigations  led  him 
into  a  multicellular  type  of  machine  having  many  pressure  stages, 
each  with  a  single  velocity  stage,  which  has  been  brought  to  a 
high  degree  of  perfection  in  France  and  is  one  of  the  best  known 
of  the  European  turbines.  It  is  also  one  of  the  few  turbines 
which  have  been  applied  to  Marine  Service.  Fig.  64  shows  a 
section  of  a  L.  P.  Rateau  turbine  as  manufactured  in  the  U.  S. 
The  H.  P.  machines  are  practically  the  same  except  for  the  num- 
ber of  stages. 

The  pressure  and  velocity  changes  are  those  shown  in  Fig.  30. 
The  running  joints  are  on  the  shaft,  where  for  a  given  clearance 
there  is  a  minimum  of  leakage.  So  many  rotating  discs  would 
appear  to  offer  large  steam  friction  loss,  but  tests  of  turbines  up  to 
1,000  and  2,000  H.  P.  show  a  friction  of  only  from  2  to  4%,  or 


COMPARISON  OF  TYPES. 


95 


about  the  same  as  drum  turbines  of  the  Parsons  type.  The 
expansion  nozzles  are  inserted  in  openings  in  the  fixed  diaphragms. 
In  the  high-pressure  stages  they  occupy  but  a  small  portion  of 
the  circumference,  but  extend  farther  around  as  the  pressure 
falls  and  the  volume  increases.  The  nozzles  or  vanes  in  each 
successive  diaphragm  are  set  around  in  angular  advance  of  the 
preceding  one,  corresponding  to  the  trajectory  of  the  steam, 
so  that  the  steam  as  it  leaves  the  moving  blades  is  opposite  the 
openings  of  the  next  expansion  set.  An  advantage  in  this 
type  is  that  the  clearance  around  the  blades  may  be  very  large, 


FIG.  64. — Section  of  Rateau  low-pressure  turbine. 

running  from  1/16  to  1/4  of  an  inch;  in  fact  the  builders  do  not 
trouble  about  giving  it  any  precise  value.  The  only  small  clear- 
ances are  at  the  hubs,  where  friction  is  less  to  be  feared.  The 
diaphragm  bushings  are  of  soft  material  with  little  attempt  at 
clearances,  for  the  machine  when  started  wears  a  sufficient  play 
to  turn  without  touching. 

The  Zoelly  turbine  has  been  mentioned  as  having  originally 
had  tangential  flow  instead  of  axial  flow.  The  old  form  had  a 
wheel  with  long  spokes  milled  on  their  faces  for  two  grooves,  which 
gave  them  a  Pelton  form  where  the  jet  impinged  upon  them. 


96 


STEAM  TURBINES. 


COMPARISON  OF  TYPES. 


97 


With  the  change  to  side  admission  the  long  spokes  were  aban- 
doned, and  as  now  built  the  Zoelly  is  a  multicellular  turbine 
differing  from  the  Rateau  only  in  its  construction  and  details. 
It  has  been  very  successful  and  is  widely  known  in  Europe. 


FIG.  66. — Section  of  A.  E.  G.  horizontal  turbine. 

As  stated  in  Art.  18,  the  Algemeine  Electricitats  Gesellschaft 
are  building  a  turbine  combining  a  Curtis  single-pressure,  multi- 
velocity  stage  wheel,  in  which  the  steam  is  expanded  to  about 


98  STEAM  TURBINES. 

atmospheric  pressure,  and  a  multicellular  low-pressure  end, 
making  a  Curtis-Rateau  machine  analogous  to  the  Curtis-Parsons 
described  in  Art.  14.  The  Bergmann  turbine  is  also  of  this  type. 
Both  are  being  built  in  large  sizes. 

Problems. 

1.  Report  on  the  A.  E.  G.  turbine  described  in  Lond.  Engineering, 
May  20,  1910,  p.  639.     Also  Power,  Feb.  7,  1911. 

2.  Report  on  the  Rateau  turbine  as  described  and  illustrated  in  Lond. 
Engineering,  May  15,  1908,  p.  639. 

3.  Report  on  the  Zoelly  turbine  as  described  and  illustrated  in  Lond. 
Engineering,  July  3,  1908,  p.  1. 

4.  Report  on  multicellular  turbine  described  in  U.  S.  Patent  issued  to 
J.  F.  M.  Patitz,  October  4,  1910.     No.  971,555. 

References. 

STODOLA:     "The  Steam  Turbine"  (4th  ed.). 

RATEAU:     Paper,  "Different  Applications  of  SteamTurbines,"     Trans. 

A.  S.  M.  E.,  vol.  xxv. 
JUDE:     "Theory  of  the  Steam  Turbine." 
REY:     Paper,  "Rateau  Steam  Turbine  and  its  Applications,"  Journal 

Am.  Soc.  Naval  Eng.,  Nov.,  1905. 
See  also  references  in  the  problems. 

Art.  21. — Special  Forms  of  Impulse -reaction  Turbine. 

The  Allis-Chalmers  turbine  shown  in  Fig.  67  is  a  single-flow 
machine  of  the  Parsons  type  differing  from  the  Westinghouse 
only  in  the  method  of  balancing,  blading,  and  in  various  details. 

In  the  typical  single-flow  Parsons  turbine  the  end  thrust  is 
carried  by  the  pistons  Pt,  P2,  and  P3  shown  in  Fig.  55.  In  the 
large  sizes  the  large  low-pressure  piston,  P3,  distorts  under  pres- 
sure and  repeated  heating  and  cooling,  so  that  it  has  been 
necessary  to  give  them  clearances  which  permit  leakage  of  steam. 
In  the  Allis  turbine  this  large  balancing  piston  is  replaced  by  a 
smaller  one,  a,  at  the  low-pressure  end  of  the  rotor  where  it  is 
practically  free  from  distortion,  and  nearly  the  whole  area  is 
effective.  In  the  later  forms  of  Westinghouse  machines  the 
balancing  is  accomplished  by  the  double  flow,  as  already  described. 
In  the  blading,  the  ends  are  riveted  to  a  channel-shaped  shroud 
ring,  B,  Fig.  68,  stiffening  them  against  vibration.  The  openings 


COMPARISON  OF  TYPES. 


99 


100 


STEAM  TURBINES. 


for  the  blade  tips  are  stamped  in  the  ring,  accurately  spacing 
the  blades.  The  shape  of  the  ring  forms  a  natural  baffle, 
and  the  clearance  may  be  smaller  than  in  previous  practice. 
Only  the  thin  edges  of  the  channel  can  touch  the  casing,  and  if 
they  do,  they  wear  free  without  any  material  heating.  The 


FIG.  68. — BJading  of  Allis-Chalmera  turbine. 


shroud  ring  itself  is  not  new,  as  both  the  Rateau  and  Zoelly 
have  used  them,  but  the  gain  from  its  use  is  greater  in  reaction 
turbines  than  in  these  types. 


Problems. 

1.  Look  up  and  report  on  the  early  history  of  steam  turbines,  see 
Neilson,  French  or  Gentsch. 

2.  Look  up  the  Elektra  turbine  described  in  Power,  April  6,  1909,  p. 
635.     Compare  with  the  new  type  of  small  Westinghouse  turbine. 

3.  Report  on  the  Wilkinson  turbine  and  small  type  of  Westinghouse 
turbine. 

4.  Report  on  the  Eyermann  turbine,  a  turbine  having  combine  radial 
and  axial  flow.     See  Power,  November  24,  1908,  p.  855. 


COMPARISON  OF  TYPES. 


101 


References. 

STODOLA:     "The  Steam  Turbine"   (4th  ed.    illustrates  and  describes 

all  the  turbines  of  any  prominence). 
JUDE:     "Theory  of  the  Steam  Turbine." 

GENTZCH:     "Steam  Turbines."     Translated  by  A.  R.  Liddell. 
SOZNOWZKI:     "Turbines  a  Vapeur,"  Paris,  1897. 
(The  last  two  are  valuable  for  the  history  of  steam  turbines.) 
See  also  references  in  the  problems. 

Art.  22. — Low-pressure  Turbines  and  Regenerators. 

Reference  to  the  pressure-temperature  curve,  Fig.  69,  or  to 
the  heat  chart,  shows  that  the  heat  drop  on  which  the  available 
energy  depends  is  greatest  at  the  low  pressures.  A  reciprocating 


Absolute  Pressures 
70      80      90      100     110    120     130    MO      160    180     170    ISO 


FIG.  69. — Pressure-temperature  curve. 


engine  is  most  efficient  at  the  higher  pressures,  down  to  about 
that  of  the  atmosphere.  The  turbine  is  most  effective  in  utilizing 
the  lower  vacuums,  as  excessive  expansion  in  an  engine  entails 


102  STEAM  TURBINES. 

prohibitive  sizes  of  L.  P.  cylinders,  and,  with  the  wide  range  of 
power  available  below  atmospheric  pressure,  it  can  be  coupled 
with  a  reciprocating  engine  to  great  advantage.  In  fact,  the 
economy  of  such  a  combined  unit  where  the  engine  exhausts  into 
a  low-pressure  turbine,  is  higher  than  when  the  entire  pres- 
sure range  from  boiler  to  condenser  is  utilized  in  an  engine  or  a 
turbine  alone,  and  the  installation  of  combined  units  of  this  kind 
is  coming  more  and  more  into  use.  For  marine  service  there  is  a 
further  advantage  of  superior  maneuvering  power  and  economy 
at  slow  speeds  over  turbines  alone,  and  the  new  White  Star 
steamers  Oceanic  and  Titanic  are  being  equipped  with  engines 
and  exhaust  turbines.  For  power  station  work  the  total  economy 
of  a  combined  unit  of  new  engines  and  new  turbines,  taking 
into  account  all  running  expenses,  fixed  charges,  etc.,  is  not  so 
high  as  for  a  H.  P.  turbine  plant  alone.  It  furnishes,  however,  a 
valuable  means  of  utilizing  existing  reciprocating  plants  and 
bringing  them  up  to  the  highest  efficiency.  Where  a  good  engine 
plant  already  exists  its  capacity  may  be  increased  more  econom- 
ically by  the  addition  of  exhaust  turbines  than  by  replacing  the 
engines  with  H.  P.  turbines. 

The  conditions  of  operation  for  exhaust  turbines  fall  under  two 
classes: 

First,  where  the  steam  supply  is  substantially  constant  or 
varies  with  the  turbine  load. 

Second,  where  it  is  widely  fluctuating  or  intermittent  and  is 
independent  of  the  turbine  load. 

In  the  first  class  fall  marine  engines  and  those  for  power  station 
service.  A  conspicuous  example  of  the  successful  installation  of 
exhaust  turbines  for  the  latter  service  is  found  in  the  Fifty-ninth 
Street  Station  of  the  Interborough  Rapid  Transit  Co.,  N.  Y. 
City. 

This  station  was  equipped  with  7500-K.  W.  compound  Corliss 
condensing  engines  direct  connected  to  generators,  each  unit 
having  two  42-inch  H.  P.  and  two  86-inch  L.  P.  cylinders,  all  of 
GO-inch  stroke,  and  an  average  steam  rate  of  17  to  18  pounds 
per  K.  W.  hour.  After  consideration  of  various  means  of  pro- 
viding additional  power,  exhaust  turbines  were  installed  on 
three  units  to  determine  their  desirability  for  the  remaining  sets. 
They  were  3-stage  vertical  Curtis  turbines,  of  7500  K.  W.  maxi- 
mum rating,  each  having  6  fixed  nozzles,  and  6  operated  by  hand 


COMPARISON  OF  TYPES.  103 

so  as  to  control  the  division  of  load  between  the  engine  and  its 
exhaust  turbine.  An  overspeed  governor  operating  a  40-inch 
butterfly  valve  on  the  steam  line  connecting  the  separator  and 
the  turbine,  and  an  8-inch  vacuum  breaker  on  the  condenser 
were  the  only  forms  of  governor  used. 

Mr.  Stott  summarizes  the  results  of  the  tests  as  follows: 

"a.  An  increase  of  100%  in  maximum  capacity  of  plant. 

"b.  An  increase  of  146%  in  economic  capacity  of  plant. 

"c.  A  saving  of  approximately  85%  of  the  condensed  steam 
for  return  to  the  boilers. 

"d.  An  average  improvement  in  economy  of  13%  over  the 
best  H.  P.  turbine  results. 

"e.  An  average  improvement  in  economy  of  25%  (between 
limits  of  7500  K.  W.  and  15000  K.  W.)  over  the  results  obtained 
by  the  engine  units  alone. 

"f.  An  average  unit  thermal  efficiency  between  the  limits  of 
6500  K.  W.  and  15500  K.  W.  of  20.6%." 

The  steam  rate  of  the  engines  alone  was  from  17  to  18  pounds 
per  K.  W.  hour,  of  the  exhaust  turbines,  26  1/2  to  28  pounds, 
and  of  the  combined  unit  ,13  to  14  pounds. 

In  an  installation  of  this  character  where  the  load  on  the 
turbine  is  electrically  connected  with  that  of  the  engine,  the 
turbine  load  rises  and  falls  with  the  steam  supply  and  no  governor 
is  required.  When  running  at  very  light  loads,  where  a  turbine 
is  inefficient,  it  is  found  economical  to  cut  it  out,  and  run  the 
engine  alone,  condensing.  Where  the  supply  of  steam  from  the 
engine  is  liable  to  long-continued  interruptions,  live  steam  can 
be  admitted  through  a  reducing  valve  from  an  independent 
source,  the  exhaust  turbine  thus  drawing  its  supply  from  two 
sources. 

The  second  class  of  installations,  where  there  is  intermittent 
steam  supply,  comprises  rolling  mills,  forging  plants,  mine  hoists, 
and  other  non-condensing  engines.  Such  engines  use  great 
quantities  of  steam  under  widely  varying  loads,  often  with  little 
or  no  expansion.  Prof.  Rateau  has  given  much  attention  to  the 
application  of  low-pressure  turbines  to  such  exhausts,  and  to 
equalize  the  supply  from  these  constantly  varying  sources  he  has 
developed  the  steam  regenerator  or  heat  accumulator,  shown  in 
Figs.  70  and  71.  The  engine  exhaust  at  about  atmospheric 
pressure  is  condensed  in  the  regenerator  when  it  arrives  in  large 


104 


STEAM  TURBINES. 


quantities,  and  revaporized  when  the  excess  ceases.  The  con- 
densation and  re-evaporation  of  the  steam  follow  the  fluctuations 
of  pressure  as  the  supply  exceeds  or  falls  short  of  that  required 
by  the  turbine. 


\Perforations  In  Mixing  Tube  for 
distributing  Steam  into  the  Water 

FIG.  70. — Side  view  of  Rateau  regenerator. 

The  regenerator  takes  a  form  like  a  tubeless  horizontal 
boiler  (Fig.  70)  where  the  water  is  kept  in  forced  circulation 
by  the  injection  of  steam.  It  is  necessary  to  provide  a  relief 
valve  to  carry  off  any  surplus  steam,  an  automatic  expansion 
valve,  as  in  the  previous  case,  to  supply  steam  directly  to 


Extension  of  Mixing  Tubes 
above  Water  Level  Leadiug 
steam  in  Regeuera 
Manifold 


Water  Level 
Baffle  Plate 


Perforations  in 
Narrowed  Portion 
of  Mixing  Tube 
for  Distribution 
of  Steam  in  the 
Water. 


FIG.  71. — Cross-section  of  Rateau  regenerator. 

the  turbine   should  the  main   engine  be  shut   down   for   any 
length  of  time,  and  check  valves  to  protect  the  regenerator  and 
main  engine  when  the  turbine  is  running  direct. 
The  steam  flow  from  the  regenerator  to  the  turbine  is  constant 


COMPARISON  OF  TYPES.  105 

compared  to  that  from  the  engine  to  the  regenerator  and  is,  of 
course,  substantially  equal  to  the  average  rate  of  engine  exhaust. 
Let  T  be  the  maximum  time,  in  minutes,  of  stoppage  of  the 
engine,  during  which  the  regenerator  must  supply  the  turbines 
alone.  Let  R  be  the  total  steam  consumption  of  the  turbine  in 
pounds  per  minute,  L  the  mean  latent  heat  at  the  regenerator 
pressures  (usually  0  to  4  pounds  gauge),  t  the  allowed  temper- 
ature drop  of  the  water.  Then 


(30) 


is  the  weight  of  water  required  to  run  the  turbine  T  minutes 
with  an  allowed  fall  in  temperature,  and  consequently  pressure. 
This  difference  in  pressure  is  not  over  3  pounds,  at  the  outside. 
The  capacity  to  absorb  the  engine  exhaust,  however,  deter- 
mines the  amount  of  water  required,  rather  than  the  question 
of  the  turbine  supply.  A  regenerator  may  be  called  on  to 
absorb  fluxes  of  steam  five  times  as  great  as  the  more  uniform 
flow  to  the  turbine  and  they  may  be  thrown  on  it  almost  instantly 
and  must  be  cared  for.  If  S  be  the  maximum  pounds  of  steam 
the  regenerator  will  be  called  on  to  absorb,  L  the  mean  latent 
heat  of  the  engine  exhaust,  and  12.4  B.  T.  U.  the  difference  in 
temperature  between  0  and  4  pounds  gauge  pressure,  then  the 
water  required  is 

'  (3D 


.  . 

which  will  usually  be  found  greatly  in  excess  of  the  w  above. 

Proper  values  of  T,  S,  and  the  mean  engine  exhaust  are 
determined  only  by  careful  investigation  for  each  installation. 
The  form  of  regenerator  shown  in  Fig.  71  has  shown  the  greatest 
capacity  for  absorbing  the  steam.  Two  regenerators  of  an  older 
type  installed  at  the  Bruay  Mines  in  France  to  utilize  the  exhaust 
of  a  hoisting  engine  and  drive  a  300  H.  P.  Rateau  generator  set 
have  been  in  successful  service  since  1902.  With  supply  pressures 
ranging  from  12  to  14.5  pounds  absolute,  and  condenser  pressures 
from  2  .  13  to  2  .  62  pounds  absolute,  the  plant  showed  a  steam  con- 
sumption of  from  37  .  4  to  45  .  2  pounds  per  E.  H.  P.  hour.  A  great 
number  of  regenerators  and  L.  P.  turbines  are  now  in  successful 


106  STEAM  TURBINES. 

use  in  Europe  and  in  this  country,  some  of   them  exceeding 
3000  H.  P.  of  turbine  capacity. 

Where  there  are  long  periods,  as  for  instance  over  night,  when 
the  exhaust  steam  supply  is  not  available,  a  high-pressure  turbine 
has  been  coupled  with  the  low-pressure  one,  the  low-pressure  tur- 
bine being  so  proportioned  that  it  can  carry  the  entire  load,  but 
if  its  steam  supply  fails  regulating  valves  controlled  by  the  speed 
and  the  pressure  in  the  regenerator,  cut  in  the  high-pressure 
turbine,  and  kept  up  the  output.  The  load  may  be  carried 


FIG.  72. — Rateau  mixed-flow  turbine. 

entirely  by  either  turbine,  or  distributed  between  them,  as  the 
momentary  conditions  require.  Any  exhaust  steam  used  in  the 
H.  P.  turbine  passes  through  the  L.  P.  one,  and  the  group  is  thus 
working  at  the  best'  economy  possible.  Running  entirely  on  the 
H.  P.  machine,  with  steam  at  110  pounds  gauge  pressure,  one  of 
the  combined  units  has  been  found  to  give  an  economy  of  about 
18  pounds  of  steam  per  E.  H.  P.  hour,  and  running  entirely  on 
the  L.  P.,  with  steam  at  atmospheric  pressure,  it  gave  about  36. 
The  two  turbines  are  now  combined  in  one  to  form  a  "mixed- 
flow"  turbine  as  shown  in  Fig.  72,  a  much  more  compact 
arrangement. 


COMPARISON  OF  TYPES.  107 

Problems. 

1.  Report  on  the  article  on  compounding  piston  engines  with  turbines, 
by  Prof.  Rateau,  Power,  October,  1907,  p.  693. 

2.  Report  on  paper  on  Exhaust  Turbines  and  Regenerators,  by  R.  F. 
Halliwell,  given  in  Lond.  Engineering,  February  5,  1909,  p.  197. 

3.  Report  on  low  pressure  steam  turbine  as  referred  to  in  article  by 
R.  M.  Neilson,  Power,  July  6,  1909,  p.  1. 

4.  Report  on    article    by  C.   H.   Smoot,   on   Regenerators.     Power, 
November  8,  1910.,  p.  1979. 

5.  Report  on  article,  L.  P.  Turbines,  by  C.  H.  Smoot,  Power,  June  22, 
1909,  p.  1100. 

6.  Report  on  investigation  into  L.  P.  turbines  for  the  Cambridge 
Elect.  Light  Co.  by  Prof.  Hollis,   see  Power,   November  10,  1908, 
p.  787. 

7.  Report   on  the   Brush-Parsons  double-flow  exhaust  turbine,  de- 
scribed in  Lond.  Engineering,  July  1,  1910,  p.  2. 

8.  Report  on  English  and  German  experience  with  L.  P.  turbines  as 
described  by  Gradenwitz  in  Engineering  Magazine,  vol.  xxxiv,  p.  278. 

9.  Report  on  the  test  of  engines  and  exhaust  turbines  at  59th  street 
Interborough    Station,   see   paper   by  Stott   and  Pigott,     Trans. 
A.  S.  M.  E.,  March,  1910,  see  also  Power,  December  14,  1909,  p.  985. 

References. 

STODOLA:     "  The  Steam  Turbine." 

MOYER:     "Steam  Turbines." 

RATEAU:   Paper,  "Different  Applications  of  Steam  Turbines,"  Trans. 

A.  S.  M.  E.,  vol.  xxv. 

RATEAU:     Article,  Power,  Oct.,  1907,  p.  693. 

BUELEIGH:  Paper  on  Exhaust  Turbines,  Power,  Oct.,  17,  1908,  p.  828. 
HALLIWELL:  Paper  on  Exhaust  Turbines,  London  Engineering,  Feb.  5, 

1909. 
STOTT  AND  PIGOTT:     Paper,  "Test  of  a  L.  P.  Turbine,"  Trans.  A.  S. 

M.  E.,  1910.     See  also  Power,  Dec.  14,  1909,  p.  985. 
SMOOT:     Articles,  Power,  June  22,    1909,  p.  1100,  and  Nov.  8,  1910, 

p.  1979. 
See  also  references  in  the  problems. 


CHAPTER  VI. 

CONDITIONS  OF  OPERATION. 
Art.  23. — Effect  of  Superheat. 

As  with  reciprocating  engines,  there  is  a  gain  in  the  economy 
of  turbines  by  the  use  of  superheated  steam,  but  how  much  is 
gained  can  not  be  fully  determined  until  the  specific  heat  of 
superheated  steam  is  definitely  known. 

While  this  has  been  the  subject  of  repeated  and  extensive 
experiments  from  the  time  of  Regnault  to  the  present,  the  proper 
values  have  not  been  agreed  upon.  Grindley  in  England; 
Greissman,  Lorenz  and  Knoblauch,  Linde  and  Klebe  in  Germany, 
and  Carpenter  and  Jones  in  America,  have  all  done  important 
work  in  this  direction,  but  the  results  are  contradictory  and 
have  not  definitely  settled  how  the  specific  heat  varies  with  the 
pressure  and  temperature  changes.  Modern  experiments  show 
that  the  value  .4805  of  Regnault  is  too  low.  Apparently  the 
specific  heat  increases  with  increase  of  pressure,  but  decreases 
with  increase  of  superheat.  This  conclusion  is  indicated  by 
Lorenz,  and  is  sustained  by  Knoblauch,  Linde,  and  Klebe. 
Mr.  Emmett  has  deduced  from  a  series  of  experiments  made  in 
a  Curtis  turbine  at  a  pressure  of  155  pounds  that  it  varies 
from  about  .  53  to  .77  for  temperatures  of  360°  to  620°  Fahr. 
The  usual  practice  is  to  take  it  as  constant  and  at  from  .  6  to  .  65. 
The  bearing  of  the  specific  heat  on  the  theoretical  economy  of 
the  turbine  using  superheated  steam  is  well  shown  by  calcula- 
tions made  on  a  De  Laval  turbine.  By  taking  first  the  water 
rate  consumption  as  a  basis  for  calculating,  the  gain  was  found 
to  be  8. 1  per  cent.  Then  on  the  basis  of  the  heat  units  in  the 
steam  the  gain  was  found  to  be,  for 


Specific  Heat 

Gain 

.48 

4.8% 

.6 

4     % 

•S 

2.7% 

108 


CONDITIONS  OP  OPERATION. 


109 


In  the  diagram  following  are  given  the  average  of  a  number 
of  steam  consumptions  for  various  degrees  of  superheat,  up  to 
200°.  These  are  based  on  tests  of  Parsons,  Curtis,  Zoelly,  and 
Brown- Boveri  turbines,  and  of  such  high  grade  engines  as  had 
records  of  tests  under  same  conditions.  The  lines  for  the  turbines 
are  more  reliable  than  for  the  engines,  being  based  on  a  larger 


I  19 

•3 


60°        80°       loo'       iao° 

Degrees  of  Superheat 
FIG.  73. — Effect  of  superheat. 


180'        SCO1 


number  of  tests.  According  to  these  curves  the  gain  in  economy 
is  greater  for  engines  than  for  turbines.  The  curves  for  the 
turbines  would  confirm  the  statement  made  by  Mr.  Parsons  and 
by  Messrs.  Dean  and  Main  that  the  gain  in  economy  is  about 
1%  for  every  10° "of  superheat,  up  to  about  150°  or  180°  Fahr. 
The  gain  from  superheat  in  turbine  practice  comes  chiefly  from 
the  reduced  steam  friction  in  the  blades  and  passages.  Refer- 
ence to  Fig.  40  shows  that  there  may  be  10%  or  15%  of  water 
in  the  steam  in  the  later  stages.  Superheating  reduces  the  con- 


110  STEAM  TURBINES. 

densation  and  by  lessening  the  water  going  through  the  blades, 
materially  decreases  the  steam  friction.  It  is  claimed  that  a 
turbine  can  operate  under  much  higher  superheat  than  an 
engine.  Doubtless  this  is  true,  but  it  remains  to  be  shown  that 
there  is  any  advantage  in  the  high  superheats  the  turbine  may 
be  made  to  stand.  The  best  practice  indicates  that  a  moderate 
superheat,  of  50°  to  100°  is  of  advantage.  Beyond  this  the 
results  are  not  wholly  favorable,  for  while  the  steam  rate  can  be 
lowered  it  is  done  at  the  expense  of  extra  fuel  required  for  the 
high  superheats. 

References. 

STODOLA:     "The  Steam  Turbine." 

JUDE:     '' Theory  of  the  Steam  Turbine." 

MOYER:     "Steam  Turbines." 

FRENCH:     " Steam  Turbines." 

MARKS  AND  DAVIS:     "Steam  Tables  and  Diagrams." 

Trans,  of  A.  S.  M.  E.,  1905  to  1910. 

Art.  24.— Relative  Effects  of  High  Vacuums  in  Reciprocating 
Engines  and  Turbines. 

The  turbine  gains  relatively  more  than  the  steam  engine  as  the 
vacuum  is  pushed  toward  its  limit.  In  fact,  this  is  one  of  the  chief 
elements  in  its  success  in  competition  with  the  older  form.  The 
advantage  in  economy,  under  equal  conditions,  is  usually  in 
favor  of  the  steam  engine  for  vacuums  lower  than  26  inches  or 
2  pounds  absolute.  For  higher  vacuums  the  turbine  gains  rap- 
idly. General  practice  has  set  the  economical  vacuum  for  recip- 
rocating engines  at  26  inches  to  27  inches.  Most  of  the  turbine 
practice  at  the  present  time  is  based  on  28  inches  to  28  1/2  inches 
of  vacuum. 

The  reasons  why  the  turbine  shows  this  greater  benefit  for  the 
higher  vacuums  are: 

First. —  The  low  temperatures  of  the  exhaust  pressure 
can  not  reach  back  into  the  hotter  parts  of  the  machine,  as 
in  a  L.  P.  engine  cylinder,  which  is  alternately  exposed  to  wide 
differences  of  temperature. 

Second. — If  expansion  is  carried  too  far  in  the  steam  engine, 
the  L.  P.  cylinder  valves  and  passages  become  abnormally  large, 
absorb  power,  and  neutralize  any  thermodynamic  gains.  A 


CONDITIONS  OF  OPERATION.  Ill 

compound  engine  with  a  cylinder  ratio  of  4  to  1,  using  steam  at 
150  pounds,  might  expand  say  15  times.  A  turbine  presents  no 
difficulties  to  an  expansion  ratio  of  100  to  110  or  down  to  a 
pressure  of  1  pound  absolute.  To  carry  this  expansion  in  a 
compound  engine  calls  for  a  cylinder  ratio  of  33  to  1,  which  is 
obviously  prohibitive. 

Since  the  expansion  of  the  engine  is  limited  to  the  L.  P.  termi- 
nal, c,  Fig.  74,  the  only  gain  in  a  higher  vacuum  is  the  lowering 
of  the  back  pressure,  represented  by  the  area  e,  d,  f,  g. 


FIG.  74. — Pressure-volume  curve  for  engines  and  turbines. 

Since  expansion  can  be  carried  down  within  a  turbine  to  the 
lowest  condenser  pressures,  the  turbines  can  utilize  the  large 
triangular  expansion  area  to  h,  in  addition  to  all  that  the  engine 
gains. 

Theoretically  the  gain  increases  very  rapidly  for  the  rarer 
vacuums,  but  with  the  turbine,  as  with  the  engine,  there  is  a 
practical  limit,  though  not  reached  so  soon,  beyond  which  the 
cost,  maintenance,  and  power  required  for  the  condensing 
apparatus  offset  the  theoretical  gains.  As  already  stated,  the 
limit  is  28  to  28  1/2  inches,  but  its  value  for  any  given  set  of  condi- 
tions is  a  question  of  engineering  economics.  Into  it  enter  the 
following: 

1.  The  steam  consumption  of 

(a)  turbine, 

(b)  auxiliaries. 

2.  The  use-factor,  or  the  ratio  of  the  actual  output  to  the 
rated  output. 

3.  The  cost  of  the  coal,  as  fired. 

4.  Cost  of  injection  water. 


112 


STEAM  TURBINES. 


5.  Fixed  charges,  on  the  condensing  plant,  covering 

(a)  Interest  on  cost. 

(b)  Interest  on  cost  of  masonry,  space  occupied,  etc. 

(c)  Depreciation  and  repairs. 

(d)  Insurance,  taxes,  etc. 

The  method  of  determining  the  economical  back  pressure  may 
be  illustrated  by  an  assumed  case.     Let 

Capacity  of  turbine  =  1,500  K.  W. 

Use-factor   (2)  =15%. 

Cost  of  coal  (3)  =  $3 . 50  per  ton,  fired. 

Suppose  fixed  charges  (5)  =  10%. 

Average  boiler  evaporation  =  7  pounds  per  pound  of  coal. 


p 
o 

Lss 

x  £ 
I 


X 

®» 


83 

53 


Vacanma 

FIG.  75. — -Approx.  relation  of  water  rate  and  vacuum. 

Let  the  cost  of  condensing  apparatus,  based  on  injection 
water  of  70°  Fahr.,  obtained  from  estimates  of  builders  for  several 
different  back  pressures,  be  as  follows:  The  plant  for  28  1/2 
inches  and  29  inches  would  be  the  same  as  for  28  inches,  except 
for  an  increase  in  the  size  of  the  dry  vacuum  pump.  These 
vacuums  are  obtainable  only  with  injection  water  of  60°  Fahr. 
for  28  1/2  inches,  and  45°-50°  for  29  inches. 


CONDITIONS  OF  OPERATION. 


113 


Inches  of 
Vacuum 

Cost  of 
Condensing 
Plant 

Increase 
in  Cost 

Increase  in 
Annual  Charge 
Based  on  10% 

26 

$6000. 

26* 

6900. 

$900. 

$90. 

27 

7500. 

600. 

60. 

27* 

8000. 

500. 

50. 

28 

9500. 

1500. 

150. 

28* 

10000. 

500. 

50. 

Let  the  guaranteed  steam  consumption  of  the  turbine  be  21 
pounds  per  K.  W.  hour,  at  28  inches  vacuum.  The  steam  rates 
for  varying  vacuums  may  be  interpolated  from  Fig.  75,  which  is 
based  on  some  Westinghouse  tests.  The  steam  consumption  of 
the  auxiliaries  may  be  based  on  their  estimated  H.  P.,  and  a 
steam  consumption  of  1  1/2  times  that  of  the  turbine. 

The  total  steam  consumption  then  would  be 


- 

Steam  Consumption 

Vacuum 

Inches 

Turbine 

Auxiliaries 

Total 

1 

2 

3 

4 

26 

23.4 

3.4   % 

24.2 

26* 

22.8 

4.      % 

23.7 

27 

22.2 

5.25% 

23.3 

27* 

21.6 

6.9   % 

23.1 

28 

20.9 

9.      % 

22.8 

28* 

20.2 

12.      % 

22.6 

The  yearly  running  cost  =  —        —  X  const.     Where 
E 

A  =K.  W.  capacity  of  the  unit. 

5  =  Total  consumption  (Coll.  4  last  table). 

(7  =  Power  factor. 

D  —  Cost  of  coal,  fired. 

E  =  Average  boiler  evaporation  per  pound. 


114 


STEAM  TURBINES. 


hours  per  year     8760 
Constant  =  —  —  =  -—=3.92. 

pounds  per  ton     2240 

Calculating  the  yearly  cost  with  the  various  consumptions, 
and  tabulating,  we  have : 


Inches  of 
Vacuum 

Cost  of  Steam 
per  Year 

Saving 

26 

440X24.2    =$10648 

26J 

440X23.7    =   10428 

$220. 

27 

440X23.3    =   10252 

176. 

27J 

440X23.1    =   10164 

88. 

28 

440X22.8    =   10032 

132. 

28J 

440X22.6    =     9944 

188. 

Comparing  these  savings  per  year  with  the  increase  in  the  annual 
charge  as  the  vacuum  varies,  we  see  that  the  gain  changes  to  a 
loss  at  just  under  28  inches.  We  see,  too,  that  if  an  ample  supply 
of  cold  injection  water  is  available,  it  would  pay  to  carry  28  1/2 


Fia.J76. — Parsons  Augmentor. 


inches  where  the  temperatures  will  permit.  This  method  would 
call  for  a  vacuum  somewhat  too  low,  if  anything,  for  the  steam 
used  in  the  auxiliaries  is  not  all  lost,  as  a  large  part  of  the  heat 
in  it  is  regained  in  heating  the  feed  water. 


CONDITIONS  OF  OPERATION.  115 

Higher  vacuums  than  28  inches  are  carried  in  high-class  power 

tations.     Some  condenser  plants  have  even  been  installed  under 

a  guarantee  to  maintain  a  working   vacuum   within  3/4  inch 

of  the  barometer.     Whether  such  a  high  vacuum  is  profitable 

remains  to  be  shown  by  experience. 

Mr.  Parsons  has  invented  a  device,  Fig.  76,  which  has  been 
widely  used  in  Europe,  but  for  some  reason  has  been  little  used  in 
this  country.  He  places  the  air  pump,  proportioned  for  about  26 
inches  vacuum,  below  the  main  condenser,  and  connects  this  by 
an  inverted  siphon,  forming  an  air  seal.  Between  the  air  pump  and 
condenser,  as  a  by-pass  connection,  is  a  steam  ejector  connection, 
A,  delivering  through  a  small  surface  condenser  B,  about  1/20 
the  size  of  the  main  one,  into  the  air  pump  suction  beyond  the 
siphon.  This  ejector  draws  nearly  all  the  residual  air  and 
vapor  from  the  main  condenser  and  increases  the  vacuum  to 
27  1/2  inches  or  28  inches,  without  the  increase  in  size  of  main 
condenser  and  air  pump  demanded  by  the  ordinary  arrangement. 
Mr.  Parsons  states  that  the  live  steam  required  by  the  ejector  is 
about  1  1/2%  of  that  used  by  the  main  turbine  at  full  load,  and 
is  materially  less  than  that  required  to  drive  the  larger  air  pump, 
which  would  regularly  be  provided  for  the  higher  vacuum. 

Problems. 

i.  Report  on  paper  of  G.  I.  Rockwood  on  "Condensers  for  Steam 
Turbines,"  Trans.  A.  S.  M.  E.,  vol.  xxvi,  p.  383. 

References. 

STODOLA:     "  The  Steam  Turbine." 
JUDE:     "Theory  of  the  Steam  Turbine." 

ROCKWOOD:    Paper,  "Condensers  for  Steam  Turbines."  Trans.  A.  S. 
M.  E.,  vol.  xxvi.  p.  383. 


CHAPTER  VII. 

POSITION  AND  FIELD  OF  THE  STEAM  TURBINE. 
Art.  25.  —  Relative  Economy  of  Engines  and  Turbines. 

The  heat  equivalent  of  a  H.  P.  hour  is 
33000  +  60 

If  H  t  and  H2  are  the  total  heats  per  pound  of  steam  before  and 
after  adiabatic  expansion  to  the  exhaust  pressure,  and  W  the 
weight  of  steam  per  H.  P.  hour  as  tested,  then 

<*.-*.>  e-~ 

or  the  available  heat  drop  X%  utilized  =  B.  T.  U.  utilized  per 
pound 

2545 


This  "potential  efficiency,"  P,  which  has  been  variously  named 
by  different  authorities,  gives  a  comparison  between  the  heat 
actually  utilized  by  the  motor,  and  that  available  under  its 
operating  conditions.  It  applies  equally  to  reciprocating 
engines,  and  to  turbines,  and  can  be  used  as  a  .basis  of  compari- 
son, provided  the  water  rate  can  be  brought  to  the  same  basis. 
The  almost  universal  basis  used  in  determining  the  economy  of 
the  reciprocating  engine  is  the  steam  rate  per  indicated  H.  P. 
hour.  No  indicator  has  been  devised  for  turbines,  and  it 
would  be  difficult  to  show  the  internal  power  developed. 
While  some  device  might  show  the  energy  of  the  jet  of  steam 
from  the  nozzle,  it  would  be  practically  impossible  to  register 
definitely  the  energy  given  up  to  the  blades  in  a  multi-stage 
turbine,  where  there  are  losses  from  eddies,  friction,  etc.  Engi- 
116 


POSITION  AND  FIELD  OF  THE  STEAM  TURBINE.    117 


neers,  however,  are  so  familiar  with  economies  based  on  indicated 
H.  P.  that  comparisons  are  often  made  by  reducing  the 
steam  consumption  of  the  turbine  to  the  basis  of  the  I.  H.  P.  of 
a  reciprocating  engine  having  the  same  electrical  output  or 
brake  H.  P.,  as  the  case  may  be.  Where  it  is  possible  there  is  a 
growing  practice  of  basing  the  steam  rate  on  the  K.  W.  hours 
or  electrical  H.  P.,  which  requires  no  assumptions,  especially  as 
the  bulk  of  turbine  work  outside  of  the  marine  service  is  in 
direct  connected  electrical  units. 

Comparisons  based  on  I.  H.  P.  must  take  into  account  the 
efficiency  of  the  generators,  turbines,  and  engines.  The  efficiencies 
of  engine-driven  generators  for  alternating  currents  on  sizes 
from  500  to  5,000  K.  W.  will  range  from  87  1/2%  at  1/4  load  up 
to  96%  at  1  1/4  load.  For  direct  current  generators,  100  K.  W. 
to  3,000  K.  W.,  it  will  range  from  89%  at  1/4  load  to  94%  at 
full  load.  The  generator  efficiency  with  the  De  Laval  units  is 
somewhat  lower,  as  the  electrical  work  is  divided  between  twin 
generators.  Their  efficiency  may  be  taken  at  from  88%  at  1/2 
load  to  91%  at  full  load,  for  direct  current,  and  at  86%  at  1/2 
load  to  92%  at  full  load. 

The  following  generator  efficiencies  are  reported  in  various 
tests. 


Capacity 

Load 

K.  W. 

i 

i 

1 

Full 

H 

Westinghouse 

1  250 

86 

93 

96 

Westinghouse  
Allis-Chalmers  
Curtis  

400 
5,500 

94.6 

97 
96 

95.7 
97.9 

96.6 
98.3 
97  5 

98.5 

In  comparing  with  engines  a  value  of  95%  may  fairly  be 
assumed.  The  mechanical  efficiency  of  reciprocating  engines 
has^been^exhaustively  investigated,  and  the  friction  losses 
appear  to  be  nearly  constant  for  all  loads.  The  efficiency  con- 
sequently falls  off  rapidly  for  light  loads.  A  summary  of  various 
modern  engines  as  given  by  French  is  as  follows : 


118  STEAM  TURBINES. 

Mechanical  Efficiency  of  Engines  at  or  near  Rating. 


Engine 

Efficiency,  % 

Engine 
alone 

Engine  and 
Generator 

96.5to97.5 
94.5 
91 
94 
87  to  93 
90 

92  to  94 
90 

Large  horizontal  Corliss,  compound  

High  speed,  simple  
Small  and  medium,  hor.  compound  

The  mechanical  efficiency  for  turbines,  as  it  involves  the  com- 
parison of  the  brake  H.  P.  with  the  indeterminate  internal 
power  developed  by  the  steam,  can  only  be  assumed.  This 
factor  is  taken  from  90%  to  95%.  For  large  units  the  higher 
figure  is  probably  nearer  correct.  These  values  give  a  combined 
efficiency  of  85%  to  93%  for  a  turbine  generating  unit,  which 
may  be  used  in  reducing  K.  W.  output  to  an  I.  H.  P.  basis,  for 
comparison  with  reciprocating  plants.  The  following  tables, 
from  a  paper  by  Mr.  C.  V.  Kerr  before  the  A.  S.  M.  E.,1  give 
means  of  comparing  reciprocating  engines  and  turbines  on  the 
basis  of  their  potential  efficiencies. 

1  Trans.  A.  S.  M.  E.,  vol.  xxv.,  1904. 


POSITION  AND  FIELD  OF  THE  STEAM  TURBINE     119 


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STEAM  TURBINES. 


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POSITION  AND  FIELD  OF  THE  STEAM  TURBINE.     121 


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122 


STEAM  TURBINES. 


Looking  at  the  economy  on  a  basis  of  steam  per  H.  P.  hour, 
the  following  table  gives  the  results  obtained  from  some  recipro- 
cating engines  of  exceptionally  high  economy. 


2 

S" 

fc 

V 

§ 

M 

I  ** 

B'   S 

Engine 

1 

£  §, 

1 
S 

S 

j! 

H 

Authority 

i 

I  o 

1 

Pk 

ji 

IB 

W 

tf 

CO 

Westinghouse  Vertical 

5400 

185 

27.3 

76 

11.93 

Eng.  Record 

Brooklyn,  N.  Y. 

May  28,  1904. 

Rockwood-WTieelock 

595 

159 

25.4 

76.4 

13. 

F.  W.  Dean 

Natick,  R.  I. 

A.  S.  M.  E.,  1895. 

Mclntosh  and  Seymour 

1076 

123 

27.1 

99.6 

20 

12.76 

F.  W.  Dean 

Webster,  Mass. 

A.  S.  M.  E.,  1898. 

Rice  and  Sargent 

627 

151 

28.6 

121 

12.1 

D.  W.  Jacobus 

Brooklyn,  N.  Y. 

A.  S.  M.  E.,  1903. 

Rice  and  Sargent 

420 

142 

25.8 

102 

297 

9.56 

D.  W.  Jacobus 

Phila.,  Pa. 

A.  S.  M.  E.,  1904. 

Horizontal  Four-  Valve 

658 

150.4 

26.4 

80 

16.4 

12.03 

Barrus'  Eng.  Tests. 

Leavitt  Pumping  Engine 

575 

175.7 

27.25    50.6 

11.2 

E.  F.  Miller 

Chestnut  Hill,  Mass. 

1 

Tech.  Quart'ly,  vol.  ix. 

The  following  is  a  table  of  tests  of  23  engines  in  commercial 
operation,  and  may  be  taken  as  indicating  average  results. 


Indicated 
Horse  Power 

Steam    per 
I.  H.  P.  Hr. 

Indicated 
Horse  Power 

Steam  per 
I.  H.  P.  Hr. 

i 

659. 

11.89 

725. 

13.27 

658. 

12.03 

1714. 

13.27 

670. 

12.29 

1030. 

13.21 

798. 

13.28 

843. 

13.53 

1017. 

13.26 

382. 

14.05 

689. 

12.69 

873. 

14.18 

708. 

12.45 

676. 

14.6 

636. 

13.28 

1540. 

14.1 

280. 

13.37 

300. 

15.78 

719. 

13.09 

606. 

16.28 

741. 

13.23 

716. 

19.36 

739. 

13.01 

In  comparison  with  these  results  are  the  following.1  In  reducing 


1  French.     "  Steam  Turbines.' 


POSITION  AND  FIELD  OF  THE  STEAM  TURBINE.     123 


the  given  steam  rates  to  I.  H.  P.  the  combined  efficiency  factors 
used  are: 


For  units  300 . 
For  units  500. 
For  units  2000 . 


.   400  K.  W oo  7o 

.1500  K.  W 90% 

.3000  K.  W 92% 


Where  93%  is  used  the  test  was  made  on  brake  H.  P.  basis. 

Engine  efficiency  alone  without  generator,  for  units  from  400 
to  500  H.  P.,  or  300  to  400  K.  W.,  taken  at  93%. 

Engine  efficiency  corresponding  to  the  300  H.  P.  De  LaVal 
turbine,  taken  at  92%. 

Typical  Steam  Consumptions  of  Turbines. 


Turbine 

Nominal 
Power 

Steam  Rate 

Estimated  Equiv. 
Consumption 
per  I.  H.  P. 

S** 
g$| 

0  ^5  W 
®    %ti 

Wl« 
SS^ 

o> 

fc 

Im 

Per  Elect. 
H.  P. 

£ 
W 

1 

Saturated  Steam 

De  Laval 

300  H.  P. 
500  H.  P. 
500  H.  P. 
500  H.  P. 
400  H.  P. 
1250  H.  P. 

15.17 
13.63 

13.96 
13.11 
14.12 
13.28 
12.68 
12.72 

92. 
88. 
88. 
90. 
93. 
90. 

Rateau  

14.9 
16.05 
14.76 

21.5 
19.78 

Zoelly  
Curtis,  American  
Westinghouse-Parsons  . 
Westinghouse-Parsons  . 

14.13 

18.95 

Moderate  Superheat 
Up  to  150° 

De  Laval        

300  H.  P. 
500  H.  P. 
500  K.  W. 
500  K.  W. 
300  K.  W. 
1500  K.  W. 
3000  K.  W. 
400  K.  W. 
1250  K.  W. 

13.94 
12.07 

14.05 
15.29 
13.28 
14.96 
13.44 
11.79 

13.78 

18.82 
20.50 
17.79 
20.06 
18. 
15.8 

18.48 

12.82 
12.36 
13.76 
11.95 
13.16 
12.10 
10.85 
11.23 
12.40 

92. 
88. 
90. 
90. 
88. 
90. 
92. 
93. 
93. 

Zoellv 

Curtis,  English  
Curtis,  American  

Parsons  
Westinghouse-Parsons  . 
Westinghouse-Parsons  . 

124  STEAM  TURBINES. 

Typical  Steam  Consumptions  of  Turbines. — Continued. 

High  Superheat 
180°  to  290° 


Curtis,  American  500  K.  W. 

11.26 

15.1 

10.14 

90. 

Curtis,  American  2000  K.  W. 

11.27,15.12 

10.36 

92. 

Parsons  3000  K.  W. 

11. 

14.74 

10.12 

92. 

Westinghouse-Parsons  .      400  K.  W. 

11.17 

10.39 

93. 

I 

In  comparison  with  the  last  test  in  the  table,  with  the  high 
super  heat,  may  be  taken  the  tests  of  a  Van  der  Kerchove  engine, 
made  by  Prof.  Schroeter. 


I.  H.  P. 

Superheat  in 
Deg.  Fahr. 

1 

Steam  per 
I.  H.  P.  Hr. 
Lbs. 

Equivalent 
Pounds  of 
Saturated 
Stm. 

Heat  Units 
per  I.  H.  P. 
Hr. 

222. 

0. 

12.06 

12.08 

250. 

226. 

43.7 

11.58 

11.77 

244. 

227. 

97.7 

11. 

11.44                  237. 

223. 

151.7 

10.67 

11.33 

234. 

223. 

221.2 

9.81 

10.69                  221. 

218. 

310.9 

1 

8.86 

10.01 

207. 

The  Rice  and  Sargent  engine,  in  table,  p.  122,  is  perhaps  a  still 
better  comparison. 

The  following  list  of  tests  of  engines  and  turbines  may  be 
taken  as  representing  the  comparative  economy  obtained  by 
each  type  to  January,  1911.  The  B.  T.  U.  per  K.  W.  minute 
are  obtained  by  multiplying  the  steam  rate  per  K.  W.  minute 
by  the  difference  between  the  B.  T.  U.  per  pound  of  steam  at  the 
initial  conditions  of  pressure  and  superheat  and  the  B.  T.  U.  in 
1  pound  of  water  at  the  vacuum  pressure,  col.  4.  The  last  column 
gives  the  best  basis  for  comparison. 


POSITION  AND  FIELD  OF  THE  STEAM  TURBINE.  125 


1 

2 

3 

4 

6 

1 

Load 
K.  W. 

Steam 
Press. 

Super- 
heat or 
Mois- 

Vacu- 
um 

Lbs 
Steam 
perK. 

B.T.U. 
per 
K.  W. 

Abs. 

ture 

. 
Hour 

Min. 

Turbines 

N.  Y.  Edison,  Westinghouse  

9870 

192 

97°F 

27.31 

15 

294 

City  Electric,  Westinghouse  9173 

182 

59° 

27.90 

14.57 

282.4 

Bklyn    Rpd.    Transit,    Westing-      11466 

192 

106° 

28.15 

14.45 

287.5 

house. 

Chgo.  Edison,  Curtis  

10186 

191 

147° 

29.47 

12.9 

270 

Carville,  Parsons  

5059.4 

209 

95° 

29.27 

13.35 

271.7 

Frankfort,  Brown-Bovari  

3521.6 

157 

130° 

28.90 

13.70 

278 

Turin,  Escher-Wyss  

3540 

187 

90° 

28.35 

15 

297.4 

Berlin  Moabit.,  A.  E.  G  

3169 

185 

215° 

29 

12.7 

268.4 

Rummelsburg,  A.  E.  G  

4239 

188 

285° 

29 

11.9 

258.5 

Engines 

N.  Y.  Edison,  Westinghouse  

3872 

200 

dry 

27 

16.78 

312 

Interborough,   59th   St.,  Allis1  .  . 

5496 

190 

dry 

25.02 

17.82 

225 

Boston  Edison,  Mclntosh  

1500 

176.5 

92° 

25.4 

16.47 

315 

Berlin  Moabit  

1920 

202.7 

223 

28 

13.35 

276 

Berlin  Luisenstrasse  |     1950 

202.7 

264 

27 

14 

295 

1 

1  Without  L.  P.  Exhaust  Turbines,  see  Art.  22. 

The  results  brought  out  in  the  foregoing  indicate 

1.  That  with  high  vacuums  the  larger  turbines  show  economies 
somewhat  better  than  reciprocating  engines. 

2.  That  with  moderate  vacuum,   in  the  medium  sizes,  the 
advantage  in  economy  still  lies  with  the  refined  types  of  recipro- 
cating engine. 

Problems. 

1.  Look  up  and  report  on  methods  of  testing  steam  turbines.     Paper 
by  Dickinson  and  Robinson,  Am.  Inst.  of  Elect.  Eng'rs,  December, 
1910. 

2.  Report  on  "Test  of  a  9000  K.  W.  Turbo-generator  Set."     Paper 
by  F.  H.  Varney,  Trans.  A.  S.  M.  E.,  vol.  xxxii,  December,  1910. 

3.  Report  on  chapters  on    testing  of    turbines  in  Moyer's  "Steam 
Turbines." 

References. 

STODOLA:     "The  Steam  Turbine." 

MOYER:     "Steam  Turbines."  '• 

JUDE:     "Theory  of  the  Steam  Turbine." 

FRENCH:     "Steam  Turbines." 


126 


STEAM  TURBINES. 


NEILSON:     "The  Steam  Turbine." 

THOMAS:     " Steam  Turbines." 

KERR:     Paper,  Trans.  A.  S.  M.  E.,  vol.  xxv. 

Art.  26. — General  Comparison  of  Engines  and  Turbines. 

Other  considerations,  however,  enter  such  as  steadiness  and 
economy  under  widely  fluctuating  working  loads,  the  room 
required,  the  foundations,  cost  of  installation  and  operation. 

The  governors  of  reciprocating  engines  regulate  the  effort 
from  stroke  to  stroke  to  meet  varying  load  conditions,  but  fluctu- 
ations due  to  the  effect  of  the  connecting  rod  and  the  weight  of 
the  reciprocating  parts  can  be  cared  for  only  by  the  flywheel. 
The  flywheel  can  at  best  only  reduce  these  fluctuations  to  within 
prescribed  limits.  In  direct  connected  generating  units,  espe- 
cially when  running  in  parallel,  the  turbine  has  the  advantage  of 
a  total  absence  of  reciprocating  motion  and  a  uniform  turning 
effort,  the  high  speed  of  the  rotor  and  heavy  armature  acting  as  a 
powerful  regulating  force.  In  fact  it  has  been  found  possible 
with  turbines  to  run  railway,  power,  and  lighting  circuits  from 
the  same  machine,  and  where  a  turbine  has  been  installed  to  run 
in  parallel  with  piston  engines  it  has  always  been  found  to  have  a 
steadying  effect  on  the  whole  system. 

But  the  turbine  is  a  one-speed  machine.  In  this  respect  it  is 
distinctly  inferior  to  the  reciprocating  engine,  for  it  cannot  be 
run  at  speeds  lower  than  that  for  which  it  is  designed  without 
serious  effect  on  its  economy.  This  is  one  of  the  limitations  to 
its  use  in  marine  work,  and  has  proved  one  of  the  difficult  prob- 
lems in  that  connection.  Even  turbine  advocates  do  not  recom- 
mend them  for  intermittent  services  and  varying  speeds.  The 
field  available  for  the  marine  turbine  seems  to  be  deep  sea  service, 
where  the  work  consists  of  long  runs  at  uniform  speed.  Tests 
made  on  a  Curtis  turbine  for  variation  in  steam  consumption  in 
relation  to  the  speed  resulted  as  follows: 


R.  P.  M. 

Steam  per  K.  W. 

hr. 

1900 

19.75 

1600 

20.74 

1300 

22.7 

1000 

27. 

POSITION  AND  FIELD  OF  THE  STEAM  TURBINE.     127 


In  the  torpedo-boat  destroyers  built  by  the  British  Navy  for 
comparing  turbines  and  reciprocating  engines,  the  turbine  boats 
were  superior  in  economy  to  the  engine-driven  boats  at  normal 
speeds,  but  invariably  inferior  when  running  at  slow  cruising 
speeds. 

In  good  practice  reciprocating  engines  are  not  installed  to  run 
under  frequent  overloads  greater  than  50%  of  the  normal 
capacity.  Corliss  engines  can  be  made  to  carry  overloads  of 
100%,  but  not  with  good  economy.  The  tendency  is  to  provide 
an  engine  large  enough  to  handle  the  maximum  loads  easily, 
and  let  it  operate  at  an  average  load  considerably  below  its  rated 
capacity.  Prof.  Carpenter  has  reported  tests  of  thirty-five  street 
railway  power  plants.  In  these  this  tendency  is  clearly  marked. 
The  following  table  gives  a  summary  of  seven  of  these  tests  made 
on  compound  condensing  engines  of  the  Corliss  or  similar  types. 
The  remaining  ones  not  given  show  the  same  tendency. 


H.  P.  of 

Mean 

%of 

Steam  per 

Engine 

observed  H.  P. 

Capacity 

I.  H.  P.  Hour. 

825 

482 

58.2 

22.7 

1,000 

277 

27.7 

21.9 

1,000 

314 

31.4 

20.0 

350 

182 

52.2 

16.64 

500 

290 

58. 

16.90 

2,000 

814 

40.7 

14.50 

200 

145 

72. 

17.30 

Average 

48  6 

18  6 

The  average  load  on  these  engines  was  less  than  half  their 
rated  capacity,  and  they  were  operated  at  an  average  steam  rate 
of  over  18  pounds  instead  of  14  and  15  pounds,  which  the  type 
of  engine  is  capable  of. 

As  turbines  have  been  rated  they  have  been  capable  of  operat- 
ing under  heavy  overloads  and  at  very  fair  steam  rates.  Guar- 
antees were  regularly  made  on  the  rates  for  overloads  of  25%, 
50%,  and  100%. 

As  a  result  turbines  have  been  installed  more  with  reference 


128  STEAM  TURBINES. 

to  the  average  load  to  be  carried,  and  less  with  reference  to  the 
maximum  load  than  a  steam  engine,  the  turbine  operating  at 
nearly  its  best  economy  most  of  the  time,  whereas  an  engine, 
rated  nearer  the  maximum  load,  would  be  operating  at  less  than 
its  most  efficient  rating. 

The  following  table  shows  the  variations  in  consumption 
reported  for  a  Westinghouse  turbine  on  loads  varying  from  1/2 
load  to  100%  overload. 


Steam  Rate 

Steam  Rate 

Load 

Saturated 

100°  Superheat 

1/2  load  
3/4  load  
Full  load  

15.86 
15.05 
13.89 

14.34 
13.45 

12.48 

1  1/4  load  
1  1/2  load  

13.85 

12.41 
12.79 

100%  overload  

15.12 

13.55 

Here  an  overload  of  100%  was  carried  with  an  increase  of  only 
10%  in  the  steam  rate.  Such  a  load  could  not  be  carried  indefi- 
nitely with  safety  to  the  generator,  but  overloads  of  50%  are 
often  met. 

It  should  be  added  however,  that  turbine  manufacturers  are 
rating  their  machines  higher  now  and  this  difference  is  becoming 
less  marked. 

In  respect  to  the  room  occupied,  the  advantage  in  favor  of  the 
turbine  alone  is  very  marked.  If  the  condensing  apparatus  be  in- 
cluded in  the  comparison  the  difference  is  not  so  great,  but  even  then 
it  is  usually  in  favor  of  the  turbine.  This  is  brought  out  clearly  in 
Fig.  77,  which  shows  a  3,500  K.  W.  engine-driven  unit, l  and  two  tur- 
bine-driven units,  one  5000  K.  W.  and  behind  one  of  7500  K.  W.  in 
the  Waterside  Station  of  the  N.  Y.  Edison  Co.  Four  of  the  engine- 
driven  units  similar  to  that  shown  in  the  picture  are  being  re- 
placed by  three  turbine  units,  each  of  20,000  K.  W.  capacity. 

A  comparison  of  these  turbine  units  with  the  reciprocating 
engine  shows  the  equally  marked  difference  in  the  foundations. 

The  selling  price  of  turbines  to-day  is  governed  largely  by  that 

1  The  engine  of  this  unit  is  really  capable  of  turning  out  6000  H.  P.,  although  the  genera- 
tor is  rated  at  3500  K.  W. 


POSITION  AND  FIELD  OF  THE  STEAM  TURBINE.     129 


130 


STEAM  TURBINES. 


of  the  competing  engines.  The  manufacturing  cost  is  probably 
less,  but  as  there  are  few  turbines  in  the  market  and  compara- 
tively little  competition  as  yet  between  them,  the  competition 
has'  been  rather  with  the  old  type  engines.  Any  estimate  of  cost, 
however,  must  include  the  land,  buildings,  and  foundations. 
These  elements  vary  so  with  different  conditions  that  no  general 
results  can  be  given.  The  general  adoption  of  the  turbine 
shows  that  for  large  units  at  least  it  is  the  cheaper,  and  it  has 
practically  driven  out  its  rival  for  large  power  station  work. 

Mr.  Stott,  Supt.  of  Motive  Power  of  the  Interborough  R.  T.  Co., 
New  York  City,  in  a  paper  before  the  A.  I.  E.  E.,  makes  the 
following  comparison  of  the  operating  cost  of  large  engine-driven 
and  turbine-driven  units.  He  says:  "The  turbine  shows  more 
uniform  steam  rate  for  varying  loads,  practically  as  good 
economy  with  saturated  steam,  and  a  thermal  economy  of  6.6% 
better  for  superheated  steam."  The  various  items  are  derived 
from  actual  costs. 

Comparison  of  Charges  per  K.  W.  Hr. 


Maintenance 


Comp. 

Cond.         Turbine 
Engine      5000  H.  P. 
7500  H.  P. 


Engine  room,  mechanical 

2  57 

51 

Boiler  room  
Coal  and  ash  handling  apparatus  
Electrical  apparatus  

4.61 
.58 
1.12 

4.30 
.54 
1.12 

Operation 

Coal  and  ash  handling  labor  

2  26 

2   11 

Removal  of  ashes  
Dock  rental  
Boiler  room,  labor  
Boiler  room,  oil,  waste,  etc  
Coal  

1.06 
.74 
7.15 
.17 
61  30 

.94 
.74 
6.68 
.17 
57  30 

Water  
Engine  room,  mechanical  labor  
Lubrication.  ... 

7.14 

6.71 
1  77 

.71 
1.35 
35 

Waste,  etc  
Electrical  labor  

.30 
2  52 

.30 
2  52 

Relative  cost  of  maintenance  and  operation  
Relative  investment  in  per  cent 

100. 
100 

79.64 
82  52 

POSITION  AND  FIELD  OF  THE  STEAM  TURBINE.     131 

The  general  statement  that  the  turbine  requires  much  less  oil 
is  borne  out  in  this  table,  where  the  turbine  requires  but  20%  of 
that  for  the  engine  generator.  In  a  turbine  oil  is  used  only  in 
the  bearings,  free  from  contact  with  the  steam,  so  that  the  steam 
is  returnable  to  the  boilers  as  soon  as  condensed,  a  property  of 
great  value  in  places  where  feed  water  is  expensive. 

Problems. 

i.  Report  on  the  power  of  plant  of  Public  Service  Corp'n.  of  N.  J., 
described  in  Power,  November  23,  1909,  p.  853. 

References. 

STEVENS  AND  HOBART:     "Steam  Turbine  Engineering." 
MOVER:     " Steam  Turbines." 
FRENCH:     " Steam  Turbines." 
MURRAY:     "  Electric  Power  Plants." 

WALDRON:     Paper,  "The  Steam  Turbine  from  an  Operating  Stand- 
point." Trans.  A.  S.  M.  E.,  vol.  xxiv. 


Art.  27. — Relative  Fields  of  Engines  and  Turbines. 

The  reciprocating  engine  is  superior  to  the  turbine  in  starting 
power,  in  reversing,  in  operating  at  varying  speeds  on  inter- 
mittent and  irregular  service.  It  requires  less  condensing 
apparatus  and  gives  a  higher  economy  for  saturated  steam  at 
average  vacuums.  It  can  run  at  moderate  speeds  and  will 
therefore  have  a  monopoly  of  many  services  where  the  high 
speeds  of  the  turbine  are  prohibitive.  These  considerations 
indicate  that  the  steam  engine  will  hold  its  place  in  locomotive 
work,  hoisting,  rolling  mills,  lighter  marine  work,  and  belt  and 
rope  driving.  Turbines  are  being  applied  to  centrifugal  air 
compressers  and  to  pumps,  with  considerable  success,  but  it  will 
be  some  time  before  they  will  be  a  serious  rival  in  this  field  or  in 
blowing  engines.  If  the  steam  engine  encounters  serious  com- 
petition in  the  smaller  sizes  for  miscellaneous  work  it  seems 
much  more  likely  that  it  will  come  from  the  gas  engine  than 
from  the  turbine. 

The  turbine,  on  the  other  hand,  has  demonstrated  that  it,  too, 
has  its  field.  For  direct  connected  services  such  as  for  generators 
and  marine  work,  especially  in  the  larger  units,  it  has  proven 


132  STEAM  TURBINES. 

superior  to  the  reciprocating  engine.     In  central  power  station 
service  it  has  practically  superseded  the  old  type  of  engine. 

Up  to  February,  1911,  the  sales  of  the  three  foremost  manu- 
facturers of  large  turbines  in  the  United  States  were  as  follows : 

General  Electric  Co.  2,150,000  K.  W. 

Westinghouse  Machine  Co.  1,600,000  K.  W. 

Allis-Chalmers  Co.  350!000  K  W- 

Total  4,100,000  K.  W. 

When  it  is  realized  that  scarcely  a  dozen  of  these  machines 
are  9  years  old,  and  the  vast  majority  not  more  than  5,  one  can 
see  the  hold  the  turbine  has  obtained  on  this  field.  About 
70  or  75%  of  the  turbines  built  are  for  electric  light,  power,  and 
traction  companies. 

Here  the  turbine  is  at  its  best.  It  is  practically  immune  from 
danger  from  priming.  Its  uniform  velocity  and  close  regulation, 
its  high  economy  under  widely  varying  loads,  its  compactness 
and  inexpensive  foundations,  and  its  exhaust  free  from  oil, 
together  with  the  great  saving  in  the  generators  due  to  the  high 
speeds,  have  made  it  distinctively  the  central  station  machine 
for  the  generation  of  alternating  current  power. 

In  marine  service  the  turbine  has  also  been  successful,  although 
its  ascendancy  here  is  not  so  marked  as  in  power  station  work. 
Mr.  C.  A.  Parsons  has  lead  the  way  into  this  field,  and  it  is  largely 
to  his  indomitable  will  that  the  successful  application  of  the 
turbine  to  marine  service  is  due.  When  he  first  began  his 
experiments,  propeller  shafts  ran  at  from  80  to  120  R.  P.  M., 
and  the  slowest  turbines  at  3,000  to  5,000  R.  P.  M.  The 
"Turbinia,"  the  first  experimental  vessel,  was  equipped  with 
2,000  H.  P.  turbines  designed  for  3,000  R.  P.  M.  It  was 
found  that  at  the  designed  speed  of  rotation  only  18  knots  could 
be  obtained.  Experimental  investigation  developed  the  exist- 
ence of  "cavitation,"  a  cylindrical  vacuum  formed  around  the 
propeller,  causing  great  loss  of  power. 

After  clever  and  extensive  experiments  propellers  were 
developed  on  new  lines,  the  power  was  divided  up  between  3 
turbines  driving  3  shafts,  the  revolutions  reduced  about  1/2, 
and  a  combination  of  turbine  and  propeller  obtained  which  gave 
remarkable  results.  A  speed  of  over  34  knots,  never  before 
reached  by  any  vessel,  was  obtained. 


POSITION  AND  FIELD  OF  .THE  STEAM  TURBINE.     133 

From  that  time,  1894,  the  development  has  been  steady. 
From  the  Turbinia,  with  its  100  feet  of  length,  9  feet  beam  and 
44  1/2  tons  displacement,  the  turbine  has  been  successfully 
applied  to  destroyers,  small  passenger  steamers  on  the  Clyde,  the 
Channel,  and  Irish  Sea  services,  to  the  Allan  liners,  the  largest 
Cunard  liners  and  to  the  heaviest  battleships.  The  Mauritania 
and  Lusitania  have  maintained  average  speeds  of  over  25  knots, 
and  developed  over  70,000  H.  P.,  70%  more  power  than  has  ever 
before  been  concentrated  in  one  set  of  engines. 

The  main  advantages  of  the  turbine  in  the  marine  service  are: 

1.  Absence  of  engine  vibration. 

2.  Lower  center  of  gravity  with  consequent  greater  stability. 

3.  Less  weight  of  machinery  with  consequent  greater  carrying 
power. 

4.  Higher  average  economy. 

5.  Smaller  propellers — and  therefore,  from  this  and  item  three, 
less  draft. 

6.  Lower  cost  of  operation — i.e.,  attendance,  supplies,  etc. 

Mr.  Parsons,  in  a  paper  before  the  Institute  of  Marine  Engi- 
neers, speaking  of  the  future  of  the  marine  turbine,  says: 

"  I  think  we  are  safe  in  predicting  that  it  will  soon  supersede 
entirely  the  reciprocating  engine  in  vessels  of  16  knots  sea-speed 
and  upward,  and  of  over  5,000  I.  H.  P.,  and  probably  also  in- 
cluding vessels  of  speed  down  to  13  knots,  of  20,000  tons  and  up- 
ward, and  possibly  still  slower  vessels  in  course  of  time.  At 
present  it  may,  I  think,  be  said  that  the  above  most  suitable  field 
comprises  about  1/5  of  the  total  steam  tonnage  of  the  world;  but 
it  must  be  remembered  that  the  speed  of  ships  tends  to  increase, 
and  the  turbine  to  improve,  and  so  the  class  of  ships  suitable  for 
the  turbine  will  increase. 

Much  interest  and  attention  are  being  centered  on  the  combina- 
tion of  reciprocating  engines  and  turbines  for  marine  work  as  in  the 
Olympic.  The  advantages  to  this  combination  have  been  con- 
sidered in  Art.  22,  but  it  seems  especially  adapted  for  ships,  giving 
high  economy  and  a  greater  flexibility  than  turbines  alone.1 

1  "Combination  System  of  Reciprocating  Engines  and  Steaui  Turbines,"  paper  by  C. 
A.  Parsons,  Institution  of  Naval  Architects.,  Lond.,  April  9,  1908.  Reprinted  in  London 
Engineering,  April  17,  1908. 

See  also  articles  on  the  Engine  of  the  White  Star  SS  "Olympic,"  London  Engineering, 
Oct.  11,  1910. 


